Theorem nfrd

Description: Consequence of the definition of not-free in a context. (Contributed by Wolf Lammen, 15-Oct-2021)

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

Proof

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