Metamath Proof Explorer


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