Theorem nf5dv

Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 18-Sep-2021) (Proof shortened by Wolf Lammen, 13-Jul-2022)

	Ref	Expression
Hypothesis	nf5dv.1	$$⊢\phi \to \left(\psi \to \forall x\psi \right)$$
Assertion	nf5dv	$$⊢\phi \to Ⅎx\psi$$

Proof

Step	Hyp	Ref	Expression
1		nf5dv.1	$$⊢\phi \to \left(\psi \to \forall x\psi \right)$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	nf5dh	$$⊢\phi \to Ⅎx\psi$$