MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.63 Unicode version

Theorem pm4.63 411
Description: Theorem *4.63 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.63  |-  ( -.  ( ph  ->  -.  ps )  <->  ( ph  /\  ps ) )

Proof of Theorem pm4.63
StepHypRef Expression
1 df-an 361 . 2  |-  ( (
ph  /\  ps )  <->  -.  ( ph  ->  -.  ps ) )
21bicomi 194 1  |-  ( -.  ( ph  ->  -.  ps )  <->  ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177    /\ wa 359
This theorem is referenced by:  pm4.67  418  nqereu  8790  axacprim  25139  andnand1  26091
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 178  df-an 361
  Copyright terms: Public domain W3C validator