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Theorem 3bitr2ri 208
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 186 . 2  |-  ( ph  <->  ch )
4 3bitr2i.3 . 2  |-  ( ch  <->  th )
53, 4bitr2i 184 1  |-  ( th  <->  ph )
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:  sbnf2  1956  ssrab  3175  rabn0m  3390  unidif0  4091  relop  4689  dmopab3  4752  issref  4921  fununi  5191  cnvoprab  6131  ssfirab  6822
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