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		df-vsca	|- .s = Slot 6
4		6nn	|- 6 e. NN
5		1lt6	|- 1 < 6
6	1 2 3 4 5	resslem	|- ( A e. V -> .x. = ( .s ` H ) )