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		pleid	|- le = Slot ( le ` ndx )
4		plendxnbasendx	|- ( le ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> .<_ = ( le ` W ) )