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

Theorem ferison 2012
Description: "Ferison", one of the syllogisms of Aristotelian logic. No 𝜑 is 𝜓, and some 𝜑 is 𝜒, therefore some 𝜒 is not 𝜓. (In Aristotelian notation, EIO-3: MeP and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
ferison.maj 𝑥(𝜑 → ¬ 𝜓)
ferison.min 𝑥(𝜑𝜒)
Assertion
Ref Expression
ferison 𝑥(𝜒 ∧ ¬ 𝜓)

Proof of Theorem ferison
StepHypRef Expression
1 ferison.maj . 2 𝑥(𝜑 → ¬ 𝜓)
2 ferison.min . 2 𝑥(𝜑𝜒)
31, 2datisi 2010 1 𝑥(𝜒 ∧ ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 97  wal 1241  wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator