Metamath Proof Explorer


Theorem impcom

Description: Importation inference with commuted antecedents. (Contributed by NM, 25-May-2005)

Ref Expression
Hypothesis imp.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion impcom ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 imp.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2 1 com12 ⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
3 2 imp ⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )