ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3bitr2ri Unicode version

Theorem 3bitr2ri 202
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitr2i.1  |-  ( ph  <->  ps )
3bitr2i.2  |-  ( ch  <->  ps )
3bitr2i.3  |-  ( ch  <->  th )
Assertion
Ref Expression
3bitr2ri  |-  ( th  <->  ph )

Proof of Theorem 3bitr2ri
StepHypRef Expression
1 3bitr2i.1 . . 3  |-  ( ph  <->  ps )
2 3bitr2i.2 . . 3  |-  ( ch  <->  ps )
31, 2bitr4i 180 . 2  |-  ( ph  <->  ch )
4 3bitr2i.3 . 2  |-  ( ch  <->  th )
53, 4bitr2i 178 1  |-  ( th  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  sbnf2  1873  ssrab  3045  rabn0m  3272  unidif0  3947  relop  4513  dmopab3  4575  issref  4734  fununi  4994  cnvoprab  5882
  Copyright terms: Public domain W3C validator