Theorem resvplusg

Description: +g is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018) (Revised by AV, 31-Oct-2024)

	Ref	Expression
Hypotheses	resvbas.1	|- H = ( G |`v A )
	resvplusg.2	|- .+ = ( +g ` G )
Assertion	resvplusg	|- ( A e. V -> .+ = ( +g ` H ) )

Proof

Step	Hyp	Ref	Expression
1		resvbas.1	|- H = ( G |`v A )
2		resvplusg.2	|- .+ = ( +g ` G )
3		plusgid	|- +g = Slot ( +g ` ndx )
4		scandxnplusgndx	|- ( Scalar ` ndx ) =/= ( +g ` ndx )
5	4	necomi	|- ( +g ` ndx ) =/= ( Scalar ` ndx )
6	1 2 3 5	resvlem	|- ( A e. V -> .+ = ( +g ` H ) )