Theorem nf5i

Description: Deduce that x is not free in ph from the definition. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nf5i.1	$$⊢\phi \to \forall x\phi$$
Assertion	nf5i	$$⊢Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		nf5i.1	$$⊢\phi \to \forall x\phi$$
2		nf5-1	$$⊢\forall x\left(\phi \to \forall x\phi \right)\to Ⅎx\phi$$
3	2 1	mpg	$$⊢Ⅎx\phi$$