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 
|- ( ph -> ps )
mpan9.2 
|- ( ch -> ( ps -> th ) )
Assertion mpan9 
|- ( ( ph /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 mpan9.1 
 |-  ( ph -> ps )
2 mpan9.2 
 |-  ( ch -> ( ps -> th ) )
3 1 2 syl5 
 |-  ( ch -> ( ph -> th ) )
4 3 impcom 
 |-  ( ( ph /\ ch ) -> th )