Metamath Proof Explorer


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 )