MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.19 Unicode version

Theorem pm5.19 351
Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.19  |-  -.  ( ph 
<->  -.  ph )

Proof of Theorem pm5.19
StepHypRef Expression
1 biid 229 . 2  |-  ( ph  <->  ph )
2 pm5.18 347 . 2  |-  ( (
ph 
<-> 
ph )  <->  -.  ( ph 
<->  -.  ph ) )
31, 2mpbi 201 1  |-  -.  ( ph 
<->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178
This theorem is referenced by:  ru  2991  pwfseqlem1  8275  bisym1  24265  rusbcALT  27038  compneOLD  27042
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
  Copyright terms: Public domain W3C validator