Theorem bj-nnfad

Description: Nonfreeness implies the equivalent of ax-5 , deduction form. See nf5rd . (Contributed by BJ, 2-Dec-2024)

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

Proof

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