Theorem resvvsca

Description: .s is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018)

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

Proof

Step	Hyp	Ref	Expression
1		resvbas.1	|- H = ( G |`v A )
2		resvvsca.2	|- .x. = ( .s ` G )
3		df-vsca	|- .s = Slot 6
4		6nn	|- 6 e. NN
5		5re	|- 5 e. RR
6		5lt6	|- 5 < 6
7	5 6	gtneii	|- 6 =/= 5
8	1 2 3 4 7	resvlem	|- ( A e. V -> .x. = ( .s ` H ) )