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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  3206  isclo2  17145  bitr3  28531  sbc3orgVD  28901  trsbcVD  28927  sbcssVD  28933  csbingVD  28934  csbsngVD  28943  csbxpgVD  28944  csbrngVD  28946  csbunigVD  28948  csbfv12gALTVD  28949  e2ebindVD  28962
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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