Theorem nfi

Description: Deduce that x is not free in ph from the definition. (Contributed by Wolf Lammen, 15-Sep-2021)

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

Proof

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