Time Jumping

John, Paul and Bob were discussing the possibility of time travel, when Bob mentioned that one of his ancestors had once gone to sleep in the 1800s, and then woken up in the 1700s.
"Okay, Bob," responded John, "I'm up to your tricks. Your ancestor must have been on a ship across the international date line from East to West on January 1, 1800."
"Oh, no," responded Bob. "Actually, he went to sleep right in his own house and woke up without having moved."
"That's ridiculous!" responded John.
"I can prove it to you," responded Bob.
How could Bob prove such a thing?

Answer:

By simply pointing out that he himself exists.

Explanation: Every one of us has ancestors who went to sleep on the last day of 1800 BC, and woke up on the first day of 1799 BC. (Of course, our ancestors would not have referred to the dates in this manner.)