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Theorem 3bitrri 206
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 184 . 2 (𝜒𝜑)
51, 4bitr3i 185 1 (𝜃𝜑)
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:  sbralie  2670  reu8  2880  unass  3233  ssin  3298  difab  3345  iunss  3854  poirr  4229  cnvuni  4725  dfco2  5038  dff1o6  5677  elznn0  9081  bj-ssom  13193
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