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Theorem 3imtr3i 199
 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 (𝜑𝜓)
3imtr3.2 (𝜑𝜒)
3imtr3.3 (𝜓𝜃)
Assertion
Ref Expression
3imtr3i (𝜒𝜃)

Proof of Theorem 3imtr3i
StepHypRef Expression
1 3imtr3.2 . . 3 (𝜑𝜒)
2 3imtr3.1 . . 3 (𝜑𝜓)
31, 2sylbir 134 . 2 (𝜒𝜓)
4 3imtr3.3 . 2 (𝜓𝜃)
53, 4sylib 121 1 (𝜒𝜃)
 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:  cbv1  1722  moimv  2063  hblem  2245  tfi  4491  smores  6182  idssen  6664  suplocsrlem  7609  bezoutlemle  11685  limcmpted  12790  sincosq3sgn  12898  subctctexmid  13185
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