Metamath Proof Explorer

Theorem mpand

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004) (Proof shortened by Wolf Lammen, 7-Apr-2013)

Ref Expression
Hypotheses mpand.1 
|- ( ph -> ps )
mpand.2 
|- ( ph -> ( ( ps /\ ch ) -> th ) )
Assertion mpand 
|- ( ph -> ( ch -> th ) )

Proof

Step Hyp Ref Expression
1 mpand.1 
 |-  ( ph -> ps )
2 mpand.2 
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )
3 2 ancomsd 
 |-  ( ph -> ( ( ch /\ ps ) -> th ) )
4 1 3 mpan2d 
 |-  ( ph -> ( ch -> th ) )