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Theorem bibi1i 226
Description: Inference adding a biconditional to the right in an equivalence. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
bibi.a  |-  ( ph  <->  ps )
Assertion
Ref Expression
bibi1i  |-  ( (
ph 
<->  ch )  <->  ( ps  <->  ch ) )

Proof of Theorem bibi1i
StepHypRef Expression
1 bicom 138 . 2  |-  ( (
ph 
<->  ch )  <->  ( ch  <->  ph ) )
2 bibi.a . . 3  |-  ( ph  <->  ps )
32bibi2i 225 . 2  |-  ( ( ch  <->  ph )  <->  ( ch  <->  ps ) )
4 bicom 138 . 2  |-  ( ( ch  <->  ps )  <->  ( ps  <->  ch ) )
51, 3, 43bitri 204 1  |-  ( (
ph 
<->  ch )  <->  ( ps  <->  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bibi12i  227  bilukdc  1328  sbrbis  1877  necon1abiddc  2308  necon1bbiddc  2309  necon4abiddc  2319  elrab3t  2749  ddifstab  3105  ssequn1  3143  asymref  4740
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