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Metamath Proof Explorer

Theorem nfv

Description: If x is not present in ph , then x is not free in ph . (Contributed by Mario Carneiro, 11-Aug-2016) Definition change. (Revised by Wolf Lammen, 12-Sep-2021)

		Ref	Expression
	Assertion	nfv	$⊢ Ⅎ x φ$

Proof

Step	Hyp	Ref	Expression
1		ax5ea	$⊢ \exists x φ \to \forall x φ$
2	1	nfi	$⊢ Ⅎ x φ$