Theorem nfd

Description: Deduce that x is not free in ps in a context. (Contributed by Wolf Lammen, 16-Sep-2021)

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

Proof

Step	Hyp	Ref	Expression
1		nfd.1	$$⊢\phi \to \left(\exists x\psi \to \forall x\psi \right)$$
2		df-nf	$$⊢Ⅎx\psi \leftrightarrow \left(\exists x\psi \to \forall x\psi \right)$$
3	1 2	sylibr	$$⊢\phi \to Ⅎx\psi$$