Metamath Proof Explorer

Theorem mpdan

Description: An inference based on modus ponens. (Contributed by NM, 23-May-1999) (Proof shortened by Wolf Lammen, 22-Nov-2012)

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

Proof

Step Hyp Ref Expression
1 mpdan.1 
 |-  ( ph -> ps )
2 mpdan.2 
 |-  ( ( ph /\ ps ) -> ch )
3 id 
 |-  ( ph -> ph )
4 3 1 2 syl2anc 
 |-  ( ph -> ch )