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Metamath Proof Explorer

Theorem nfa1

Description: The setvar x is not free in A. x ph . (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 11-Sep-2021) Remove dependency on ax-12 . (Revised by Wolf Lammen, 12-Oct-2021)

		Ref	Expression
	Assertion	nfa1	$⊢ Ⅎ x \forall x φ$

Proof

Step	Hyp	Ref	Expression
1		alex	$⊢ \forall x φ \leftrightarrow \neg \exists x \neg φ$
2		nfe1	$⊢ Ⅎ x \exists x \neg φ$
3	2	nfn	$⊢ Ⅎ x \neg \exists x \neg φ$
4	1 3	nfxfr	$⊢ Ⅎ x \forall x φ$