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		tsetid	|- TopSet = Slot ( TopSet ` ndx )
4		tsetndxnbasendx	|- ( TopSet ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> J = ( TopSet ` H ) )