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Theorem ferison 2315
 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(φ χ)
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(φ χ)
31, 2datisi 2313 1 x(χ ¬ ψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358  ∀wal 1540  ∃wex 1541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by: (None)
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