Metamath Proof Explorer


Theorem nfth

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 12-Sep-2021)

Ref Expression
Hypothesis nfth.1 ⊢ 𝜑
Assertion nfth Ⅎ 𝑥 𝜑

Proof

Step Hyp Ref Expression
1 nfth.1 ⊢ 𝜑
2 nftht ⊢ ( ∀ 𝑥 𝜑 → Ⅎ 𝑥 𝜑 )
3 2 1 mpg ⊢ Ⅎ 𝑥 𝜑