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Theorem bitr3 28571
Description: Closed nested implication form of bitr3i 242. Derived automatically from bitr3VD 28941. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bitr3  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  ->  ( ps 
<->  ch ) ) )

Proof of Theorem bitr3
StepHypRef Expression
1 bibi1 317 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  <->  ( ps  <->  ch ) ) )
21biimpd 198 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  ch )  ->  ( ps 
<->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  3orbi123VD  28942  sbc3orgVD  28943  trsbcVD  28969  csbrngVD  28988  e2ebindVD  29004  e2ebindALT  29022
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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