Theorem bj-nnfa

Description: Nonfreeness implies the equivalent of ax-5 . See nf5r , nf5ri . (Contributed by BJ, 28-Jul-2023)

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

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	simprbi	$$⊢Ⅎ\text{'}x\phi \to \left(\phi \to \forall x\phi \right)$$