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Theorem 3bitr3rd 218
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 189 . 2  |-  ( ph  ->  ( ch  <->  th )
)
51, 4bitr3d 189 1  |-  ( ph  ->  ( ta  <->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> 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:  funconstss  5538  eqneg  8499  minclpr  11015  evenennn  11913
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