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Theorem 3imtr3i 200
Description: A mixed syllogism inference, useful for removing a definition from both sides of an implication. (Contributed by NM, 10-Aug-1994.)
Hypotheses
Ref Expression
3imtr3.1  |-  ( ph  ->  ps )
3imtr3.2  |-  ( ph  <->  ch )
3imtr3.3  |-  ( ps  <->  th )
Assertion
Ref Expression
3imtr3i  |-  ( ch 
->  th )

Proof of Theorem 3imtr3i
StepHypRef Expression
1 3imtr3.2 . . 3  |-  ( ph  <->  ch )
2 3imtr3.1 . . 3  |-  ( ph  ->  ps )
31, 2sylbir 135 . 2  |-  ( ch 
->  ps )
4 3imtr3.3 . 2  |-  ( ps  <->  th )
53, 4sylib 122 1  |-  ( ch 
->  th )
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:  cbv1  1755  cbv1v  1757  moimv  2102  hblem  2295  tfi  4593  smores  6307  idssen  6791  suplocsrlem  7821  bezoutlemle  12023  limcmpted  14485  sincosq3sgn  14602  subctctexmid  15104  dcapnconstALT  15164
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