No proof for that, especially when both "Lord" and "God" are said
to Jesus.
Certainly it is not a proof. It is an inference from points 1 and 2.
Points 1 and 2, however, are
facts, not inferences.
Certainly point 3 could be wrong. I just think it very unlikely to be wrong in view of the unequivocal veracity of points 1 and 2.
Other
alternative explanations, which we could explore, are:
1.
Jesus didn't know Thomas' true beliefs. Thomas had been hiding them from Jesus.
2. The God of Thomas was the Father at the time Jesus resurrected, but then
Thomas changed his mind. Two suboptions from this are
2.1 Thomas changed his mind within the period of 8 days.
2.2 Thomas changed his mind when he realized Jesus was alive
3. In John 20:17 Jesus was saying
who their God should be, regardless of their current beliefs. Then we have other 3 suboptions
3.1 The woman did not communicate this to the apostles
3.2 The woman did it, but since Thomas was away, Thomas didn't get the message.
3.3 The woman did it, and Thomas got the message, but he didn't believe in the woman nor in the message.
4. Jesus and his disciples
did not share with the rest of Israel the idea of God. There are 2 suboptions here
4.1 They thought that "God" meant "divine", an attribute or class. Therefore, YHWH was a title that could be given to several persons. What the Shema Israel of the Torah really meant was: "Listen, Israel, YHWH our God, is a Council of Divine persons who act as One"
4.2. They thought that The Father and the Son were in reality the same Person. Therefore, when Jesus said "I am ascending to My Father", he meant "I am ascending to another aspect of Me".