Theorem bj-nnfad

Description: Nonfreeness implies the equivalent of ax-5 , deduction form. See nf5rd . (Contributed by BJ, 2-Dec-2023)

	Ref	Expression
Hypothesis	bj-nnfad.1	⊢ ( 𝜑 → Ⅎ' 𝑥 𝜓 )
Assertion	bj-nnfad	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-nnfad.1	⊢ ( 𝜑 → Ⅎ' 𝑥 𝜓 )
2		bj-nnfa	⊢ ( Ⅎ' 𝑥 𝜓 → ( 𝜓 → ∀ 𝑥 𝜓 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )