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Theorem 3bitrri 205
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitri.1  |-  ( ph  <->  ps )
3bitri.2  |-  ( ps  <->  ch )
3bitri.3  |-  ( ch  <->  th )
Assertion
Ref Expression
3bitrri  |-  ( th  <->  ph )

Proof of Theorem 3bitrri
StepHypRef Expression
1 3bitri.3 . 2  |-  ( ch  <->  th )
2 3bitri.1 . . 3  |-  ( ph  <->  ps )
3 3bitri.2 . . 3  |-  ( ps  <->  ch )
42, 3bitr2i 183 . 2  |-  ( ch  <->  ph )
51, 4bitr3i 184 1  |-  ( th  <->  ph )
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:  reu8  2789  unass  3130  ssin  3195  difab  3240  iunss  3727  poirr  4070  cnvuni  4549  dfco2  4850  dff1o6  5447  elznn0  8447  bj-ssom  10889
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