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Theorem wl-bibi1 24289
Description: Theorem *4.86 of [WhiteheadRussell] p. 122. Place this (and the following theorems) after bitr1. [ +22] (Contributed by NM, 3-Jan-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
wl-bibi1  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )

Proof of Theorem wl-bibi1
StepHypRef Expression
1 bicom1 192 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
2 wl-bitr1 24286 . . 3  |-  ( ( ps  <->  ph )  ->  (
( ph  <->  ch )  ->  ( ps 
<->  ch ) ) )
31, 2syl 17 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  ->  ( ps 
<->  ch ) ) )
4 wl-bitr1 24286 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ps  <->  ch )  ->  ( ph  <->  ch )
) )
53, 4impbid 185 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178
This theorem is referenced by:  wl-bibi1i  24290  wl-bibi1d  24291
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
  Copyright terms: Public domain W3C validator