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Metamath Proof Explorer

Theorem bj-nnfa

Description: Nonfreeness implies the equivalent of ax-5 . See nf5r . (Contributed by BJ, 28-Jul-2023)

		Ref	Expression
	Assertion	bj-nnfa	$⊢ Ⅎ' x φ \to (φ \to \forall x φ)$

Step	Hyp	Ref	Expression
1		df-bj-nnf	$⊢ Ⅎ' x φ \leftrightarrow ((\exists x φ \to φ) \land (φ \to \forall x φ))$
2	1	simprbi	$⊢ Ⅎ' x φ \to (φ \to \forall x φ)$