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Theorem wl-bitr 24330
Description: Theorem *4.22 of [WhiteheadRussell] p. 117. Replace. [ -4] (Contributed by NM, 3-Jan-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
wl-bitr  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  ch )
)  ->  ( ph  <->  ch ) )

Proof of Theorem wl-bitr
StepHypRef Expression
1 wl-bitr1 24320 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ps  <->  ch )  ->  ( ph  <->  ch )
) )
21imp 418 1  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  ch )
)  ->  ( ph  <->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
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  df-an 360
  Copyright terms: Public domain W3C validator