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Metamath Proof Explorer

Theorem nfal

Description: If x is not free in ph , then it is not free in A. y ph . (Contributed by Mario Carneiro, 11-Aug-2016)

		Ref	Expression
	Hypothesis	nfal.1	$⊢ Ⅎ x φ$
	Assertion	nfal	$⊢ Ⅎ x \forall y φ$

Step	Hyp	Ref	Expression
1		nfal.1	$⊢ Ⅎ x φ$
2	1	nf5ri	$⊢ φ \to \forall x φ$
3	2	hbal	$⊢ \forall y φ \to \forall x \forall y φ$
4	3	nf5i	$⊢ Ⅎ x \forall y φ$