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Theorem bitr 691
Description: Theorem *4.22 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
bitr  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  ch )
)  ->  ( ph  <->  ch ) )

Proof of Theorem bitr
StepHypRef Expression
1 bibi1 319 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )
21biimpar 473 1  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  ch )
)  ->  ( ph  <->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  opelopabt  4277  domunfican  7125  albitr  26958  aiffbbtat  27249  aisbbisfaisf  27250  abnotbtaxb  27264  3orbi123VD  27895
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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