Theorem ressle

Description: le is unaffected by restriction. (Contributed by Mario Carneiro, 3-Nov-2015)

	Ref	Expression
Hypotheses	ressle.1	|- W = ( K |`s A )
	ressle.2	|- .<_ = ( le ` K )
Assertion	ressle	|- ( A e. V -> .<_ = ( le ` W ) )

Proof

Step	Hyp	Ref	Expression
1		ressle.1	|- W = ( K |`s A )
2		ressle.2	|- .<_ = ( le ` K )
3		df-ple	|- le = Slot ; 1 0
4		10nn	|- ; 1 0 e. NN
5		1lt10	|- 1 < ; 1 0
6	1 2 3 4 5	resslem	|- ( A e. V -> .<_ = ( le ` W ) )