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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  2705  unass  3068  ssin  3127  difab  3174  iunss  3661  poirr  4007  cnvuni  4436  dfco2  4735  dff1o6  5329  elznn0  7834  bj-ssom  8320
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