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Theorem 3bitr3rd 217
Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitr3d.1  |-  ( ph  ->  ( ps  <->  ch )
)
3bitr3d.2  |-  ( ph  ->  ( ps  <->  th )
)
3bitr3d.3  |-  ( ph  ->  ( ch  <->  ta )
)
Assertion
Ref Expression
3bitr3rd  |-  ( ph  ->  ( ta  <->  th )
)

Proof of Theorem 3bitr3rd
StepHypRef Expression
1 3bitr3d.3 . 2  |-  ( ph  ->  ( ch  <->  ta )
)
2 3bitr3d.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
3 3bitr3d.2 . . 3  |-  ( ph  ->  ( ps  <->  th )
)
42, 3bitr3d 188 . 2  |-  ( ph  ->  ( ch  <->  th )
)
51, 4bitr3d 188 1  |-  ( ph  ->  ( ta  <->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> 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:  funconstss  5317  eqneg  7887  evenennn  10731
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