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Metamath Proof Explorer

Theorem bj-nnfea

Description: Nonfreeness implies the equivalent of ax5ea . (Contributed by BJ, 28-Jul-2023)

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

Step	Hyp	Ref	Expression
1		bj-nnfe	$⊢ Ⅎ' x φ \to (\exists x φ \to φ)$
2		bj-nnfa	$⊢ Ⅎ' x φ \to (φ \to \forall x φ)$
3	1 2	syld	$⊢ Ⅎ' x φ \to (\exists x φ \to \forall x φ)$