Theorem elpwi2OLD

Description: Obsolete version of elpwi2 as of 26-May-2024. (Contributed by Glauco Siliprandi, 3-Mar-2021) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	elpwi2.1	|- B e. V
	elpwi2.2	|- A C_ B
Assertion	elpwi2OLD	|- A e. ~P B

Proof

Step	Hyp	Ref	Expression
1		elpwi2.1	|- B e. V
2		elpwi2.2	|- A C_ B
3		elpw2g	|- ( B e. V -> ( A e. ~P B <-> A C_ B ) )
4	1 3	ax-mp	|- ( A e. ~P B <-> A C_ B )
5	2 4	mpbir	|- A e. ~P B