This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem bj-nnfeai

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

		Ref	Expression
	Hypothesis	bj-nnfeai.1	$⊢ Ⅎ' x φ$
	Assertion	bj-nnfeai	$⊢ \exists x φ \to \forall x φ$

Step	Hyp	Ref	Expression
1		bj-nnfeai.1	$⊢ Ⅎ' x φ$
2		bj-nnfea	$⊢ Ⅎ' x φ \to (\exists x φ \to \forall x φ)$
3	1 2	ax-mp	$⊢ \exists x φ \to \forall x φ$