Theorem bj-nnfead

Description: Nonfreeness implies the equivalent of ax5ea , deduction form. (Contributed by BJ, 2-Dec-2023)

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

Proof

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