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' 𝑥 𝜑
Assertion	bj-nnfai	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bj-nnfai.1	⊢ Ⅎ' 𝑥 𝜑
2		bj-nnfa	⊢ ( Ⅎ' 𝑥 𝜑 → ( 𝜑 → ∀ 𝑥 𝜑 ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )