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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  3177  isclo2  17111  bitr3  28308  sbc3orgVD  28676  trsbcVD  28702  sbcssVD  28708  csbingVD  28709  csbsngVD  28718  csbxpgVD  28719  csbrngVD  28721  csbunigVD  28723  csbfv12gALTVD  28724  e2ebindVD  28737
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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