Theorem bj-elpwgALT

Description: Alternate proof of elpwg . See comment for bj-velpwALT . (Contributed by BJ, 17-Jan-2025) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	bj-elpwgALT	|- ( A e. V -> ( A e. ~P B <-> A C_ B ) )

Proof

Step	Hyp	Ref	Expression
1		eleq1	|- ( x = A -> ( x e. ~P B <-> A e. ~P B ) )
2		sseq1	|- ( x = A -> ( x C_ B <-> A C_ B ) )
3		bj-velpwALT	|- ( x e. ~P B <-> x C_ B )
4	1 2 3	vtoclbg	|- ( A e. V -> ( A e. ~P B <-> A C_ B ) )