Theorem ressmulr

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

	Ref	Expression
Hypotheses	ressmulr.1	|- S = ( R |`s A )
	ressmulr.2	|- .x. = ( .r ` R )
Assertion	ressmulr	|- ( A e. V -> .x. = ( .r ` S ) )

Proof

Step	Hyp	Ref	Expression
1		ressmulr.1	|- S = ( R |`s A )
2		ressmulr.2	|- .x. = ( .r ` R )
3		df-mulr	|- .r = Slot 3
4		3nn	|- 3 e. NN
5		1lt3	|- 1 < 3
6	1 2 3 4 5	resslem	|- ( A e. V -> .x. = ( .r ` S ) )