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 = x A φ

Proof

Step Hyp Ref Expression
1 ne0i x A A
2 1 necon2bi A = ¬ x A
3 2 pm2.21d A = x A φ
4 3 ralrimiv A = x A φ