ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3bitrri GIF version

Theorem 3bitrri 207
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 185 . 2 (𝜒𝜑)
51, 4bitr3i 186 1 (𝜃𝜑)
Colors of variables: wff set class
Syntax hints:  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  sbralie  2721  reu8  2933  unass  3292  ssin  3357  difab  3404  iunss  3927  poirr  4306  cnvuni  4812  dfco2  5127  dff1o6  5774  elznn0  9264  bj-ssom  14548
  Copyright terms: Public domain W3C validator