There are more than just that fragment........however, the Muratorian is not THE bible
The manuscripts can be seen in part on Wiki among other places
The document contains a list of the books of the New Testament, a similar list concerning the Old Testament having apparently preceded it. It dates from around 170AD.....way after the Peshitta and the Old Latin Vulgate.
145 AD Peshitta is the Syriac version of the NT. Peshitta means “straight or rule, and set the standard because of it’s early composition and strong agreement with the Greek text underlying the KJV. Antioch is in Syria and was the seat of all Christian doctrine.
Justin Martyr mentions the gospels as being FOUR in number and quotes from them, also quotes some of the epistles of Paul and from the Revelation of John
Early church fathers quoted so extensively from the New Testament in their writings that it is said the entire NT can be reproduced from their writings alone.
NT books were in existence in their present form at the close of the apostolic age (end of 1st century)
150 AD Tatian’s Diatesseron
150 AD Itala bible the bible of the Baptists, first used by early Christians and Waldenses. Translated from the TR
157 AD Old Latin Vulgate (original Vulgate, not the corrupt version by Jerome)
135-200AD Iraenaeus quoted from all the NT books except Philemon, Jude, James, and 3 John
160-224 AD Tertulllian, a contemporary of Origen and Clement mentions all the NT books except 2 Peter, James and 2 John
165-220 AD Clement of Alexandria names all the books of the NT except Philemon, James, 2 Peter and 3 John. According to Eusebius, Clement gave explanations and quoted from ALL canonical books.