Theorem resshom

Description: Hom is unaffected by restriction. (Contributed by Mario Carneiro, 5-Jan-2017)

	Ref	Expression
Hypotheses	resshom.1	|- D = ( C |`s A )
	resshom.2	|- H = ( Hom ` C )
Assertion	resshom	|- ( A e. V -> H = ( Hom ` D ) )

Proof

Step	Hyp	Ref	Expression
1		resshom.1	|- D = ( C |`s A )
2		resshom.2	|- H = ( Hom ` C )
3		df-hom	|- Hom = Slot ; 1 4
4		1nn0	|- 1 e. NN0
5		4nn	|- 4 e. NN
6	4 5	decnncl	|- ; 1 4 e. NN
7		1nn	|- 1 e. NN
8		4nn0	|- 4 e. NN0
9		1lt10	|- 1 < ; 1 0
10	7 8 4 9	declti	|- 1 < ; 1 4
11	1 2 3 6 10	resslem	|- ( A e. V -> H = ( Hom ` D ) )