Theorem ressip

Description: The inner product is unaffected by restriction. (Contributed by Thierry Arnoux, 16-Jun-2019)

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

Proof

Step	Hyp	Ref	Expression
1		resssca.1	|- H = ( G |`s A )
2		ressip.2	|- ., = ( .i ` G )
3		ipid	|- .i = Slot ( .i ` ndx )
4		ipndxnbasendx	|- ( .i ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> ., = ( .i ` H ) )