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Metamath Proof Explorer

Theorem mpan9

Description: Modus ponens conjoining dissimilar antecedents. (Contributed by NM, 1-Feb-2008) (Proof shortened by Andrew Salmon, 7-May-2011)

Ref Expression
Hypotheses mpan9.1 ⊢ φ → ψ
mpan9.2 ⊢ χ → ψ → θ
Assertion mpan9 ⊢ φ ∧ χ → θ

Proof

Step Hyp Ref Expression
1 mpan9.1 ⊢ φ → ψ
2 mpan9.2 ⊢ χ → ψ → θ
3 1 2 syl5 ⊢ χ → φ → θ
4 3 impcom ⊢ φ ∧ χ → θ