Theorem bj-nnfai

Description: Nonfreeness implies the equivalent of ax-5 , inference form. See nf5ri . (Contributed by BJ, 22-Sep-2024)

	Ref	Expression
Hypothesis	bj-nnfai.1	$$⊢Ⅎ\text{'}x\phi$$
Assertion	bj-nnfai	$$⊢\phi \to \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		bj-nnfai.1	$$⊢Ⅎ\text{'}x\phi$$
2		bj-nnfa	$$⊢Ⅎ\text{'}x\phi \to \left(\phi \to \forall x\phi \right)$$
3	1 2	ax-mp	$$⊢\phi \to \forall x\phi$$