ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3imtr3i GIF version

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 (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 133 . 2 (𝜒𝜓)
4 3imtr3.3 . 2 (𝜓𝜃)
53, 4sylib 120 1 (𝜒𝜃)
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  1673  moimv  2008  hblem  2187  tfi  4331  smores  5941  idssen  6324  bezoutlemle  10541
  Copyright terms: Public domain W3C validator