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

Theorem pm4.24 643
Description: Theorem *4.24 of [WhiteheadRussell] p. 117. (Contributed by NM, 11-May-1993.)
Assertion
Ref Expression
pm4.24  |-  ( ph  <->  (
ph  /\  ph ) )

Proof of Theorem pm4.24
StepHypRef Expression
1 id 22 . 2  |-  ( ph  ->  ph )
21pm4.71i 632 1  |-  ( ph  <->  (
ph  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  anidm  644  anabsan  809  nic-ax  1480  sbnf2  2144  euind  3151  reuind  3167  disjprg  4293  wesn  4915  sqrlem5  12741  crngunit  16759  lmodvscl  16970  isclo2  18697  vitalilem1  21093  ercgrg  22974  slmdvscl  26235  prtlem16  29019
  Copyright terms: Public domain W3C validator