MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  anabs7 Unicode version

Theorem anabs7 785
Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 17-Nov-2013.)
Assertion
Ref Expression
anabs7  |-  ( ( ps  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )

Proof of Theorem anabs7
StepHypRef Expression
1 simpr 447 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
21pm4.71ri 614 . 2  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ( ph  /\ 
ps ) ) )
32bicomi 193 1  |-  ( ( ps  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358
This theorem is referenced by:  prtlem15  26846  un2122  28879
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator