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Metamath Proof Explorer

Theorem hbnae

Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in Megill p. 446 (p. 14 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker hbnaev when possible. (Contributed by NM, 13-May-1993) (New usage is discouraged.)

Ref Expression
Assertion hbnae ⊢ ¬ ∀ x x = y → ∀ z ¬ ∀ x x = y

Proof

Step Hyp Ref Expression
1 hbae ⊢ ∀ x x = y → ∀ z ∀ x x = y
2 1 hbn ⊢ ¬ ∀ x x = y → ∀ z ¬ ∀ x x = y