Theorem toponrestid

Description: Given a topology on a set, restricting it to that same set has no effect. (Contributed by Jim Kingdon, 6-Jul-2022)

	Ref	Expression
Hypothesis	toponrestid.t	|- A e. ( TopOn ` B )
Assertion	toponrestid	|- A = ( A |`t B )

Proof

Step	Hyp	Ref	Expression
1		toponrestid.t	|- A e. ( TopOn ` B )
2	1	toponunii	|- B = U. A
3	2	restid	|- ( A e. ( TopOn ` B ) -> ( A |`t B ) = A )
4	1 3	ax-mp	|- ( A |`t B ) = A
5	4	eqcomi	|- A = ( A |`t B )