Metamath Proof Explorer

Theorem hbnaev

Description: Any variable is free in -. A. x x = y , if x and y are distinct. This condition is dropped in hbnae , at the expense of more axiom dependencies. Instance of naev2 . (Contributed by NM, 13-May-1993) (Revised by Wolf Lammen, 9-Apr-2021)

Ref Expression
Assertion hbnaev ¬ x x = y z ¬ x x = y


Step Hyp Ref Expression
1 naev2 ¬ x x = y z ¬ x x = y