Metamath Proof Explorer


Theorem ancoms

Description: Inference commuting conjunction in antecedent. (Contributed by NM, 21-Apr-1994)

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

Proof

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