Theorem ressunif

Description: UnifSet is unaffected by restriction. (Contributed by Thierry Arnoux, 7-Dec-2017)

	Ref	Expression
Hypotheses	ressunif.1	|- H = ( G |`s A )
	ressunif.2	|- U = ( UnifSet ` G )
Assertion	ressunif	|- ( A e. V -> U = ( UnifSet ` H ) )

Proof

Step	Hyp	Ref	Expression
1		ressunif.1	|- H = ( G |`s A )
2		ressunif.2	|- U = ( UnifSet ` G )
3		unifid	|- UnifSet = Slot ( UnifSet ` ndx )
4		unifndxnbasendx	|- ( UnifSet ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> U = ( UnifSet ` H ) )