MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  anabss4 Structured version   Unicode version

Theorem anabss4 790
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.)
Hypothesis
Ref Expression
anabss4.1  |-  ( ( ( ps  /\  ph )  /\  ps )  ->  ch )
Assertion
Ref Expression
anabss4  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabss4
StepHypRef Expression
1 anabss4.1 . . 3  |-  ( ( ( ps  /\  ph )  /\  ps )  ->  ch )
21anabss1 789 . 2  |-  ( ( ps  /\  ph )  ->  ch )
32ancoms 441 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
This theorem is referenced by:  anabss7  796  ordtri3or  4642
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362
  Copyright terms: Public domain W3C validator