Metamath Proof Explorer

Theorem anabsi8

Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999)

Ref Expression
Hypothesis anabsi8.1 
|- ( ps -> ( ( ps /\ ph ) -> ch ) )
Assertion anabsi8 
|- ( ( ph /\ ps ) -> ch )

Proof

Step Hyp Ref Expression
1 anabsi8.1 
 |-  ( ps -> ( ( ps /\ ph ) -> ch ) )
2 1 anabsi5 
 |-  ( ( ps /\ ph ) -> ch )
3 2 ancoms 
 |-  ( ( ph /\ ps ) -> ch )