Description: Alternate proof of eq0 . Shorter, but requiring df-clel , ax-8 . (Contributed by NM, 29-Aug-1993) Avoid ax-11 , ax-12 . (Revised by GG and Steven Nguyen, 28-Jun-2024) (Proof modification is discouraged.) (New usage is discouraged.)
|- ( A = (/) <-> A. x -. x e. A )
|- ( A = (/) <-> A. x ( x e. A <-> x e. (/) ) )
|- -. x e. (/)
|- ( -. x e. A <-> ( x e. A <-> x e. (/) ) )
|- ( A. x -. x e. A <-> A. x ( x e. A <-> x e. (/) ) )