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	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
Assertion	nf5i	⊢ Ⅎ 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		nf5i.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2		nf5-1	⊢ ( ∀ 𝑥 ( 𝜑 → ∀ 𝑥 𝜑 ) → Ⅎ 𝑥 𝜑 )
3	2 1	mpg	⊢ Ⅎ 𝑥 𝜑