Metamath Proof Explorer

Theorem impcom

Description: Importation inference with commuted antecedents. (Contributed by NM, 25-May-2005)

Ref Expression
Hypothesis imp.1 
|- ( ph -> ( ps -> ch ) )
Assertion impcom 
|- ( ( ps /\ ph ) -> ch )

Proof

Step Hyp Ref Expression
1 imp.1 
 |-  ( ph -> ( ps -> ch ) )
2 1 com12 
 |-  ( ps -> ( ph -> ch ) )
3 2 imp 
 |-  ( ( ps /\ ph ) -> ch )