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Metamath Proof Explorer

Theorem nfa1-o

Description: x is not free in A. x ph . (Contributed by Mario Carneiro, 11-Aug-2016) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		hba1-o	$⊢ \forall x φ \to \forall x \forall x φ$
2	1	nf5i	$⊢ Ⅎ x \forall x φ$