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Theorem bibi1 318
Description: Theorem *4.86 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
bibi1  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )

Proof of Theorem bibi1
StepHypRef Expression
1 id 20 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21bibi1d 311 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177
This theorem is referenced by:  bitr  690  sbeqalb  3158  isclo2  17077  bitr3  27938  sbc3orgVD  28306  trsbcVD  28332  sbcssVD  28338  csbingVD  28339  csbsngVD  28348  csbxpgVD  28349  csbrngVD  28351  csbunigVD  28353  csbfv12gALTVD  28354  e2ebindVD  28367
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
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