Theorem nfri

Description: Consequence of the definition of not-free. (Contributed by Wolf Lammen, 16-Sep-2021)

	Ref	Expression
Hypothesis	nfri.1	$$⊢Ⅎx\phi$$
Assertion	nfri	$$⊢\exists x\phi \to \forall x\phi$$

Proof

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