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Theorem bibi1 317
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 19 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21bibi1d 310 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  bitr  689  sbeqalb  3045  isclo2  16827  bitr3  28328  sbc3orgVD  28700  trsbcVD  28726  sbcssVD  28732  csbingVD  28733  csbsngVD  28742  csbxpgVD  28743  csbrngVD  28745  csbunigVD  28747  csbfv12gALTVD  28748  e2ebindVD  28761
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 177
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