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Metamath Proof Explorer

Theorem nfn

Description: Inference associated with nfnt . (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 18-Sep-2021)

Ref Expression
Hypothesis nfn.1 ⊢ Ⅎ 𝑥 𝜑
Assertion nfn Ⅎ 𝑥 ¬ 𝜑

Proof

Step Hyp Ref Expression
1 nfn.1 ⊢ Ⅎ 𝑥 𝜑
2 nfnt ⊢ ( Ⅎ 𝑥 𝜑 → Ⅎ 𝑥 ¬ 𝜑 )
3 1 2 ax-mp ⊢ Ⅎ 𝑥 ¬ 𝜑