Theorem bj-nnfe

Description: Nonfreeness implies the equivalent of ax5e . (Contributed by BJ, 28-Jul-2023)

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

Proof

Step	Hyp	Ref	Expression
1		df-bj-nnf	$$⊢Ⅎ\text{'}x\phi \leftrightarrow \left(\left(\exists x\phi \to \phi \right)\wedge \left(\phi \to \forall x\phi \right)\right)$$
2	1	simplbi	$$⊢Ⅎ\text{'}x\phi \to \left(\exists x\phi \to \phi \right)$$