Theorem ressplusg

Description: +g is unaffected by restriction. (Contributed by Stefan O'Rear, 27-Nov-2014)

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

Proof

Step	Hyp	Ref	Expression
1		ressplusg.1	|- H = ( G |`s A )
2		ressplusg.2	|- .+ = ( +g ` G )
3		plusgid	|- +g = Slot ( +g ` ndx )
4		basendxnplusgndx	|- ( Base ` ndx ) =/= ( +g ` ndx )
5	4	necomi	|- ( +g ` ndx ) =/= ( Base ` ndx )
6	1 2 3 5	resseqnbas	|- ( A e. V -> .+ = ( +g ` H ) )