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Theorem bocardo 2316
 Description: "Bocardo", one of the syllogisms of Aristotelian logic. Some φ is not ψ, and all φ is χ, therefore some χ is not ψ. (In Aristotelian notation, OAO-3: MoP and MaS therefore SoP.) For example, "Some cats have no tails", "All cats are mammals", therefore "Some mammals have no tails". A reorder of disamis 2314; prefer using that instead. (Contributed by David A. Wheeler, 28-Aug-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
bocardo.maj x(φ ¬ ψ)
bocardo.min x(φχ)
Assertion
Ref Expression
bocardo x(χ ¬ ψ)

Proof of Theorem bocardo
StepHypRef Expression
1 bocardo.maj . 2 x(φ ¬ ψ)
2 bocardo.min . 2 x(φχ)
31, 2disamis 2314 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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