And therefore did the Jews persecute Jesus, and sought to slay him, because he had done these things on the sabbath day. But Jesus answered them, My Father worketh hitherto, and I work. Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God. (John 5:16-18)
a) God is my Father
b) My Father works on the Sabbath
c) I also therefore work on the Sabbath
Or, since God can work on the Sabbath then so can I. This second argument that Jesus makes in verse 17 is reached by combining sentences B and C above. From these two propositions in verse 17, we must understand Jesus to be saying that it is within His right to do what God is doing (i.e. working on the Sabbath). Therefore, it’s good, necessary and not unreasonable to arrive at the inference that Jesus thinks that He and God are equals. Incidentally Jesus confirms this interpretation of John 5:17 when He states in Matthew 12:8 that “The Son of man is Lord even of the Sabbath.” How can a mere man claim to have authority over an ordinance (the Sabbath) that was instituted by God if the man Himself is not God?
My Father has been working until now, and I have been working: In our terminology, Jesus would say: “My Father works on the Sabbath, and so do I.” By this Jesus makes it clear that He is equal to God the Father, and reminds us that God doesn’t take holidays. – Guzik Commentary on O.T. and N.T.
The interpretation of the Jews was a very natural and just one. He not only said that God was his Father, but he said that he had the same right to work on the Sabbath that God had; that by the same authority, and in the same manner, he could dispense with the obligation of the day. – Albert Barnes’ Notes on the Bible
Only God could dispense with the obligation of keeping the Sabbath; by Jesus admission that He works (and has been working until now) on the Sabbath we are right to necessarily conclude that Jesus was claiming to be equal with God.