Theorem rzalALT

Description: Alternate proof of rzal . Shorter, but requiring df-clel , ax-8 . (Contributed by NM, 11-Mar-1997) (Proof shortened by Andrew Salmon, 26-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	rzalALT	|- ( A = (/) -> A. x e. A ph )

Proof

Step	Hyp	Ref	Expression
1		ne0i	|- ( x e. A -> A =/= (/) )
2	1	necon2bi	|- ( A = (/) -> -. x e. A )
3	2	pm2.21d	|- ( A = (/) -> ( x e. A -> ph ) )
4	3	ralrimiv	|- ( A = (/) -> A. x e. A ph )