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Theorem 3bitrri 196
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitri.1 (𝜑𝜓)
3bitri.2 (𝜓𝜒)
3bitri.3 (𝜒𝜃)
Assertion
Ref Expression
3bitrri (𝜃𝜑)

Proof of Theorem 3bitrri
StepHypRef Expression
1 3bitri.3 . 2 (𝜒𝜃)
2 3bitri.1 . . 3 (𝜑𝜓)
3 3bitri.2 . . 3 (𝜓𝜒)
42, 3bitr2i 174 . 2 (𝜒𝜑)
51, 4bitr3i 175 1 (𝜃𝜑)
Colors of variables: wff set class
Syntax hints:  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  reu8  2737  unass  3100  ssin  3159  difab  3206  iunss  3698  poirr  4044  cnvuni  4521  dfco2  4820  dff1o6  5416  elznn0  8258  bj-ssom  10033
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