Theorem bj-nnfeai

Description: Nonfreeness implies the equivalent of ax5ea , inference form. (Contributed by BJ, 22-Sep-2024)

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

Proof

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