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Metamath Proof Explorer

Theorem hbn1

Description: Alias for ax-10 to be used instead of it. (Contributed by NM, 24-Jan-1993) (Proof shortened by Wolf Lammen, 18-Aug-2014)

		Ref	Expression
	Assertion	hbn1	$⊢ \neg \forall x φ \to \forall x \neg \forall x φ$

Step	Hyp	Ref	Expression
1		ax-10	$⊢ \neg \forall x φ \to \forall x \neg \forall x φ$