Theorem bj-nnfea

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

	Ref	Expression
Assertion	bj-nnfea	$$⊢Ⅎ\text{'}x\phi \to \left(\exists x\phi \to \forall x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-nnfe	$$⊢Ⅎ\text{'}x\phi \to \left(\exists x\phi \to \phi \right)$$
2		bj-nnfa	$$⊢Ⅎ\text{'}x\phi \to \left(\phi \to \forall x\phi \right)$$
3	1 2	syld	$$⊢Ⅎ\text{'}x\phi \to \left(\exists x\phi \to \forall x\phi \right)$$