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Theorem 3bitr3ri 209
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
3bitr3i.1  |-  ( ph  <->  ps )
3bitr3i.2  |-  ( ph  <->  ch )
3bitr3i.3  |-  ( ps  <->  th )
Assertion
Ref Expression
3bitr3ri  |-  ( th  <->  ch )

Proof of Theorem 3bitr3ri
StepHypRef Expression
1 3bitr3i.3 . 2  |-  ( ps  <->  th )
2 3bitr3i.1 . . 3  |-  ( ph  <->  ps )
3 3bitr3i.2 . . 3  |-  ( ph  <->  ch )
42, 3bitr3i 184 . 2  |-  ( ps  <->  ch )
51, 4bitr3i 184 1  |-  ( th  <->  ch )
Colors of variables: wff set class
Syntax hints:    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bigolden  897  sb9  1897  sbcco  2837  dfiin2g  3713  dffun6f  4939
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