Theorem resstset

Description: TopSet is unaffected by restriction. (Contributed by Mario Carneiro, 13-Aug-2015)

	Ref	Expression
Hypotheses	resstset.1	|- H = ( G |`s A )
	resstset.2	|- J = ( TopSet ` G )
Assertion	resstset	|- ( A e. V -> J = ( TopSet ` H ) )

Proof

Step	Hyp	Ref	Expression
1		resstset.1	|- H = ( G |`s A )
2		resstset.2	|- J = ( TopSet ` G )
3		df-tset	|- TopSet = Slot 9
4		9nn	|- 9 e. NN
5		1lt9	|- 1 < 9
6	1 2 3 4 5	resslem	|- ( A e. V -> J = ( TopSet ` H ) )