MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.24 Unicode version

Theorem pm4.24 627
Description: Theorem *4.24 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.24  |-  ( ph  <->  (
ph  /\  ph ) )

Proof of Theorem pm4.24
StepHypRef Expression
1 id 21 . 2  |-  ( ph  ->  ph )
21pm4.71i 616 1  |-  ( ph  <->  (
ph  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360
This theorem is referenced by:  anidm  628  anabsan  789  nic-ax  1433  euind  2889  reuind  2903  disjprg  3916  wesn  4668  sqrlem5  11609  crngunit  15279  lmodvscl  15479  isclo2  16657  vitalilem1  18795  iscola2  25258  prtlem16  25903
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
  Copyright terms: Public domain W3C validator