Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl6bir GIF version

Theorem syl6bir 157
 Description: A mixed syllogism inference. (Contributed by NM, 18-May-1994.)
Hypotheses
Ref Expression
syl6bir.1 (𝜑 → (𝜒𝜓))
syl6bir.2 (𝜒𝜃)
Assertion
Ref Expression
syl6bir (𝜑 → (𝜓𝜃))

Proof of Theorem syl6bir
StepHypRef Expression
1 syl6bir.1 . . 3 (𝜑 → (𝜒𝜓))
21biimprd 151 . 2 (𝜑 → (𝜓𝜒))
3 syl6bir.2 . 2 (𝜒𝜃)
42, 3syl6 33 1 (𝜑 → (𝜓𝜃))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 102 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105 This theorem depends on definitions:  df-bi 114 This theorem is referenced by:  exdistrfor  1697  cbvexdh  1817  repizf2  3943  issref  4735  fnun  5033  ovigg  5649  tfrlem9  5966  tfri3  5984  ordge1n0im  6050  nntri3or  6103  axprecex  7012  peano5nnnn  7024  peano5nni  7993  zeo  8402  nn0ind-raph  8414  fzm1  9064  fzind2  9197  fzfig  9370  bcpasc  9634  climrecvg1n  10098  oddnn02np1  10192  oddge22np1  10193  evennn02n  10194  evennn2n  10195  bj-intabssel  10315
 Copyright terms: Public domain W3C validator