Theorem ressvsca

Description: .s is unaffected by restriction. (Contributed by Mario Carneiro, 7-Dec-2014)

	Ref	Expression
Hypotheses	resssca.1	|- H = ( G |`s A )
	ressvsca.2	|- .x. = ( .s ` G )
Assertion	ressvsca	|- ( A e. V -> .x. = ( .s ` H ) )

Proof

Step	Hyp	Ref	Expression
1		resssca.1	|- H = ( G |`s A )
2		ressvsca.2	|- .x. = ( .s ` G )
3		vscaid	|- .s = Slot ( .s ` ndx )
4		vscandxnbasendx	|- ( .s ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> .x. = ( .s ` H ) )