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	$$⊢\forall z\neg \forall xx=y\to \phi$$
Assertion	hbnaes	$$⊢\neg \forall xx=y\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		hbnaes.1	$$⊢\forall z\neg \forall xx=y\to \phi$$
2		hbnae	$$⊢\neg \forall xx=y\to \forall z\neg \forall xx=y$$
3	2 1	syl	$$⊢\neg \forall xx=y\to \phi$$