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Theorem bibi1i 227
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 139 . 2  |-  ( (
ph 
<->  ch )  <->  ( ch  <->  ph ) )
2 bibi.a . . 3  |-  ( ph  <->  ps )
32bibi2i 226 . 2  |-  ( ( ch  <->  ph )  <->  ( ch  <->  ps ) )
4 bicom 139 . 2  |-  ( ( ch  <->  ps )  <->  ( ps  <->  ch ) )
51, 3, 43bitri 205 1  |-  ( (
ph 
<->  ch )  <->  ( ps  <->  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bibi12i  228  biadani  601  bilukdc  1374  sbrbis  1934  necon1abiddc  2370  necon1bbiddc  2371  necon4abiddc  2381  elrab3t  2839  ddifstab  3208  ssequn1  3246  asymref  4924
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