Theorem bj-nnfed

Description: Nonfreeness implies the equivalent of ax5e , deduction form. (Contributed by BJ, 2-Dec-2023)

	Ref	Expression
Hypothesis	bj-nnfed.1	$$⊢\phi \to Ⅎ\text{'}x\psi$$
Assertion	bj-nnfed	$$⊢\phi \to \left(\exists x\psi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-nnfed.1	$$⊢\phi \to Ⅎ\text{'}x\psi$$
2		bj-nnfe	$$⊢Ⅎ\text{'}x\psi \to \left(\exists x\psi \to \psi \right)$$
3	1 2	syl	$$⊢\phi \to \left(\exists x\psi \to \psi \right)$$