Metamath Proof Explorer

Theorem mpanl1

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Wolf Lammen, 7-Apr-2013)

Ref Expression
Hypotheses mpanl1.1 
|- ph
mpanl1.2 
|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion mpanl1 
|- ( ( ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 mpanl1.1 
 |-  ph
2 mpanl1.2 
 |-  ( ( ( ph /\ ps ) /\ ch ) -> th )
3 1 jctl 
 |-  ( ps -> ( ph /\ ps ) )
4 3 2 sylan 
 |-  ( ( ps /\ ch ) -> th )