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Theorem 3imtr3i 198
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 133 . 2  |-  ( ch 
->  ps )
4 3imtr3.3 . 2  |-  ( ps  <->  th )
53, 4sylib 120 1  |-  ( ch 
->  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:  cbv1  1676  moimv  2011  hblem  2192  tfi  4370  smores  6011  idssen  6446  bezoutlemle  10872
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