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		df-unif	|- UnifSet = Slot ; 1 3
4		1nn0	|- 1 e. NN0
5		3nn	|- 3 e. NN
6	4 5	decnncl	|- ; 1 3 e. NN
7		1nn	|- 1 e. NN
8		3nn0	|- 3 e. NN0
9		1lt10	|- 1 < ; 1 0
10	7 8 4 9	declti	|- 1 < ; 1 3
11	1 2 3 6 10	resslem	|- ( A e. V -> U = ( UnifSet ` H ) )