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Are you really that dense?
The fact that he wrote his gospel at all is solid evidence that he was a Cohen.
The other two synoptics were taken largely from Matthews work and attributed to Luke and Mark. Its possible that Luke really did write his, but most unlikely that the very immature and flippant John Mark wrote anything.
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You claimed in post 68 that the gospel in the original language provided proof that Matthew was a Cohen. So provide your proof. If it means I need to add another book or two to my library, I will gladly shell out the dough.
That he wrote something is not of itself proof. Perhaps you are familiar with Salome Alexandra? Her rule led to extremely widespread education in her domains, kicking off a golden age of learning for the common man whose effects would extend into the time of Our Lord.
By the way, your “flippant John Mark” is likely also a Levite, given that he is kin to Barnabas, who was also a Levite. Lovely how you feel free to pick and choose among the Biblical books.