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Theorem 3bitrrd 213
Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitrd.1  |-  ( ph  ->  ( ps  <->  ch )
)
3bitrd.2  |-  ( ph  ->  ( ch  <->  th )
)
3bitrd.3  |-  ( ph  ->  ( th  <->  ta )
)
Assertion
Ref Expression
3bitrrd  |-  ( ph  ->  ( ta  <->  ps )
)

Proof of Theorem 3bitrrd
StepHypRef Expression
1 3bitrd.3 . 2  |-  ( ph  ->  ( th  <->  ta )
)
2 3bitrd.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
3 3bitrd.2 . . 3  |-  ( ph  ->  ( ch  <->  th )
)
42, 3bitr2d 187 . 2  |-  ( ph  ->  ( th  <->  ps )
)
51, 4bitr3d 188 1  |-  ( ph  ->  ( ta  <->  ps )
)
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:  srpospr  7073  divap0b  7890  divfl0  9430  cjreb  9954
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