Theorem resvbas

Description: Base 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 )
	resvbas.2	|- B = ( Base ` G )
Assertion	resvbas	|- ( A e. V -> B = ( Base ` H ) )

Proof

Step	Hyp	Ref	Expression
1		resvbas.1	|- H = ( G |`v A )
2		resvbas.2	|- B = ( Base ` G )
3		baseid	|- Base = Slot ( Base ` ndx )
4		scandxnbasendx	|- ( Scalar ` ndx ) =/= ( Base ` ndx )
5	4	necomi	|- ( Base ` ndx ) =/= ( Scalar ` ndx )
6	1 2 3 5	resvlem	|- ( A e. V -> B = ( Base ` H ) )