Metamath Proof Explorer


Theorem hbnaes

Description: Rule that applies hbnae to antecedent. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 15-May-1993) (New usage is discouraged.)

Ref Expression
Hypothesis hbnaes.1
|- ( A. z -. A. x x = y -> ph )
Assertion hbnaes
|- ( -. A. x x = y -> ph )

Proof

Step Hyp Ref Expression
1 hbnaes.1
 |-  ( A. z -. A. x x = y -> ph )
2 hbnae
 |-  ( -. A. x x = y -> A. z -. A. x x = y )
3 2 1 syl
 |-  ( -. A. x x = y -> ph )