Well, there's plenty of internal evidence in the Gospels to that effect . . . e.g. John 19:35.
But C.S. Lewis has pointed out an interesting proof that does not depend upon the good faith (or cunning) of the authors of the Gospels. He points out that they are written in a colloquial, somewhat rough, reportorial style, and that they contain a lot of minutiae of the sort that you acquire by observation (e.g. Jesus "doodling" in the sand in John 8:6).
If somebody had set out to start a new religion by making it up out of whole cloth, they would have followed the more high-flown and rhetorical models of the classical authors, to give the account more credence (from their society's point of view.) In other words, if the Gospels are fiction and not factual reporting, they anticipated the style of the naturalistic 20th century novel by about 2000 years.
I didn't say the Gospels were fiction. I asked about a source that they were written by eyewitnesses. I'm a l;azy researcher, but I recall my readings that they were written at the end of the first century and in the second. I welcome evidence to the contrary.
PS: I have read several authors of fiction who wrote in the style as you described, as if they were there or eyewitness.
However,(and this is REALLY cool!) When you go to the gospel of Luke, it bears the marks of a well educated, proper speaking person who was well versed in Greek....., in the first chapter (what you would expect from a physician... educated, right?). The second chapter lapses back into what I call "pidgin" Greek, and reads more like John, or Mark. Then, after the events of the nativity, the styliltic, classically influenced Greek picks up (I took a year of classical Greek in undergrad, and about 4 years more Koine Gk. in grad school). My own theory is that Luke, who spoke very good greek, was "transcribing" word for word the events of the nativity from someone. Who better to give the details, and who better to know some of the more intimate details of Mary's heart revealed there, than Mary herself? She would have been old by this time, but still just a Hebrew peasant, whose Greek would have been stammering and poor. Look at the Christmas story in Luke, look at the personal details that only would have been know my Mary, and then visualize someone "switching on" a foreign voice with bad grammar and uneducated style being quoted directly. I think we got Mary's direct story That is my theory of the lapse into "bad" Greek for Luke 2, anyway. It is a cool theory, even if unprovable.