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

Theorem 3imtr3i 189
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 125 . 2 (χψ)
4 3imtr3.3 . 2 (ψθ)
53, 4sylib 127 1 (χθ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  cbv1  1629  moimv  1963  hblem  2142  tfi  4248  smores  5848  idssen  6193
  Copyright terms: Public domain W3C validator