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Metamath Proof Explorer

Theorem bj-nnfai

Description: Nonfreeness implies the equivalent of ax-5 , inference form. See nf5ri . (Contributed by BJ, 22-Sep-2024)

		Ref	Expression
	Hypothesis	bj-nnfai.1	$⊢ Ⅎ' x φ$
	Assertion	bj-nnfai	$⊢ φ \to \forall x φ$

Step	Hyp	Ref	Expression
1		bj-nnfai.1	$⊢ Ⅎ' x φ$
2		bj-nnfa	$⊢ Ⅎ' x φ \to (φ \to \forall x φ)$
3	1 2	ax-mp	$⊢ φ \to \forall x φ$