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Theorem ferison 2606
 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 2604 1 𝑥(𝜒 ∧ ¬ 𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 383  ∀wal 1521  ∃wex 1744 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745 This theorem is referenced by: (None)
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