Smullyan's Drinking Principle/Informal Proof

Informal Proof
There are two cases:


 * $(1): \quad$ Everyone in the pub is drinking.
 * $(2): \quad$ Someone in the pub is not drinking.

Suppose first that everyone in the pub is drinking.

Then $x$ can be chosen to be any person in the pub.

Suppose instead that someone in the pub is not drinking.

Then $x$ can be chosen to be any person in the pub who is not drinking.