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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  3043  isclo2  16825  bitr3  28272  sbc3orgVD  28627  trsbcVD  28653  sbcssVD  28659  csbingVD  28660  csbsngVD  28669  csbxpgVD  28670  csbrngVD  28672  csbunigVD  28674  csbfv12gALTVD  28675  e2ebindVD  28688
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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