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Theorem 3imtr3d 202
Description: More general version of 3imtr3i 200. Useful for converting conditional definitions in a formula. (Contributed by NM, 8-Apr-1996.)
Hypotheses
Ref Expression
3imtr3d.1  |-  ( ph  ->  ( ps  ->  ch ) )
3imtr3d.2  |-  ( ph  ->  ( ps  <->  th )
)
3imtr3d.3  |-  ( ph  ->  ( ch  <->  ta )
)
Assertion
Ref Expression
3imtr3d  |-  ( ph  ->  ( th  ->  ta ) )

Proof of Theorem 3imtr3d
StepHypRef Expression
1 3imtr3d.2 . 2  |-  ( ph  ->  ( ps  <->  th )
)
2 3imtr3d.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3imtr3d.3 . . 3  |-  ( ph  ->  ( ch  <->  ta )
)
42, 3sylibd 149 . 2  |-  ( ph  ->  ( ps  ->  ta ) )
51, 4sylbird 170 1  |-  ( ph  ->  ( th  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  f1imass  5774  focdmex  6115  tposfn2  6266  eroveu  6625  ismkvnex  7152  indpi  7340  axcaucvglemres  7897  qsqeqor  10627  caucvgrelemcau  10984  m1dvdsndvds  12242  pcpremul  12287  pcaddlem  12332  pockthlem  12348  limccnpcntop  14037  sincosq1sgn  14140  sincosq2sgn  14141  subctctexmid  14632  neap0mkv  14698
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