MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  anabs1 Structured version   Unicode version

Theorem anabs1 785
Description: Absorption into embedded conjunct. (Contributed by NM, 4-Sep-1995.) (Proof shortened by Wolf Lammen, 16-Nov-2013.)
Assertion
Ref Expression
anabs1  |-  ( ( ( ph  /\  ps )  /\  ph )  <->  ( ph  /\ 
ps ) )

Proof of Theorem anabs1
StepHypRef Expression
1 simpl 445 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21pm4.71i 615 . 2  |-  ( (
ph  /\  ps )  <->  ( ( ph  /\  ps )  /\  ph ) )
32bicomi 195 1  |-  ( ( ( ph  /\  ps )  /\  ph )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360
This theorem is referenced by:  poirr  4517  mndcl  14700  frgra3v  28466  uun121p1  28970
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