Berachot 15a

Berachot 15a

Rabbi Chiya bar Abba cited Rabbi Yochanan:
One who wishes to accept upon himself the yoke of the kingship of Heaven completely, {Brachot 15a} should go to the bathroom, wash his hands, put on tefillin, read Shema, and pray, and this is the complete yoke of the kingship of Heaven.
And anyone who goes to the bathroom, washes his hands, puts on tefillin, reads Shema, and prays, the Scripture considers it as if he has built an altar {in a good way --mizbeach} and sacrificed upon it a sacrifice, as it states in Tehillim 26:6:

ו אֶרְחַץ בְּנִקָּיוֹן כַּפָּי; וַאֲסֹבְבָה אֶת-מִזְבַּחֲךָ ה.

6 I will wash my hands in innocency; so will I compass Thine altar, O LORD,

Rav read kriat Shema, donned tefillin, and then prayed. And we conclude that it was the messenger who was at fault, for he delayed in bringing the tefillin until after he [Rav] had read kriat Shema, and so he interrupted and donned tefillin so as not to pray without tefillin.

And it is found written in the name of Rabbi Yitzchak za'l, son of Rabbi Yehuda, that the messenger brought him his tallit after kriat Shema and he wrapped himself in the tallit and prayed. And he brought a support to his words from this of Rav, that he donned tefillin between kriat Shema and tefillah, and the same would be true for tzitzit.

And it seems that there is room to differentiate, for tefillin are different, as is stated [in the continuation of the gemara]:

If he put on tefillin, read Shema, and pray, and this is the complete yoke of the kingship of Heaven.

And furthermore, it seems that from logic, there is to differentiate, for tefillin are different in that there is written in them the acceptance of the yoke of kingship of Heaven and the yoke of the commandments, and the Scriptures called them a remembrance.

And furthermore, this is a mitzvah with the body of a person, but the mitzvah of tzitzit is not in his body, but rather that the Scripture requires it in the garment which happens to have four corners, and if he did not wear it now, he will wear it after a time.

And [so], one should not interrupt between kriat Shema and tefillah for the sake of wrapping oneself in a tallit.

Ravina said to Rava: Does Master see this member of the Rabbinate who has come from the West {=Israel} and said: one who does not have water to wash can rub his hands with a pebble, or dirt, or sawdust?
He {Rava} said: He says well. Does it (the pasuk in Tehillim 26:6) say beMayim - with water? It says בְּנִקָּיוֹן - in cleanliness. Any substance which cleans.

Rav Chisda would curse anyone who looked after water at the time of prayer.

Rosh: There are some seforim in which is written "And these words are in terms of reading Shema but for prayer {=Shemoneh Esrei}, he needs to go back {looking for water to clean your hands}. For Resh Lakish said: for kneading {betahara} and for netila {before eating} and for praying {with a tzibbur}, four mil." As we learn in Pesachim, perek Elu Ovrin (daf 46a) and in Chullin perek haOr vehaRotev (da 122b). 

And the Rif as well wrote so, and this girsa is not found in old sefarim. And also [Rashi] did not explain [have a girsa] of this. And it seems that he was not gores this, for {it doesn't make sense, for just as} he should not go back at the time of kriat Shema, so that the zman would not pass, so too would be the case in terms of tefillah, for why should one differentiate one from the other? And even though kriat Shema is Biblical while tefillah is Rabbinic, the Sages gave strength to their words just as for Torah.

And Rashi as well does not explain there {in Pesachim} a reason for tefillah {going back} as because of netilat yadayim, but rather in order to pray with ten. And so too later on in perek Mi Shemetu (daf 22a) it is stated 'they cancelled the washing like Rav Chisda, for Rav Chisda cursed one who went back for water at time of prayer', and it does not mention kriat Shema at all.

MISHNA:

IF ONE RECITES THE SHEMA' WITHOUT HEARING WHAT HE SAYS,
HE HAS PERFORMED HIS OBLIGATION.
R. JOSE SAYS: HE HAS NOT PERFORMED HIS OBLIGATION.

IF HE RECITES IT WITHOUT PRONOUNCING THE LETTERS CORRECTLY,
R. JOSE SAYS THAT HE HAS PERFORMED HIS OBLIGATION,
R. JUDAH SAYS THAT HE HAS NOT PERFORMED HIS OBLIGATION.

IF HE RECITES IT BACKWARD {out of order}
HE HAS NOT PERFORMED HIS OBLIGATION.

IF HE RECITES IT AND MAKES A MISTAKE HE GOES BACK TO THE PLACE WHERE HE MADE THE MISTAKE.

Rabbenu Moshe za'l wrote that if he did not read the parshiyot in order, he fulfills, for behold in the Torah, they are not written in order. Even though we learn in a Mishna "why is Shema said before vehaya im shamoa", it is only lechatchila that its order is such, but the seder is not meakev. And this that Rabbi Yehuda said that between Vayomer and Emes veYatziv one should not interrupt, this is when one reads the parshiyot in order of the institution of the Chachamim.