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