Metamath Proof Explorer


Theorem anidms

Description: Inference from idempotent law for conjunction. (Contributed by NM, 15-Jun-1994)

Ref Expression
Hypothesis anidms.1 ⊢ ( ( 𝜑 ∧ 𝜑 ) → 𝜓 )
Assertion anidms ( 𝜑 → 𝜓 )

Proof

Step Hyp Ref Expression
1 anidms.1 ⊢ ( ( 𝜑 ∧ 𝜑 ) → 𝜓 )
2 1 ex ⊢ ( 𝜑 → ( 𝜑 → 𝜓 ) )
3 2 pm2.43i ⊢ ( 𝜑 → 𝜓 )