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Theorem celaront 2306
 Description: "Celaront", one of the syllogisms of Aristotelian logic. No φ is ψ, all χ is φ, and some χ exist, therefore some χ is not ψ. (In Aristotelian notation, EAO-1: MeP and SaM therefore SoP.) For example, given "No reptiles have fur", "All snakes are reptiles.", and "Snakes exist.", prove "Some snakes have no fur". Note the existence hypothesis. Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 27-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
celaront.maj x(φ → ¬ ψ)
celaront.min x(χφ)
celaront.e xχ
Assertion
Ref Expression
celaront x(χ ¬ ψ)

Proof of Theorem celaront
StepHypRef Expression
1 celaront.maj . 2 x(φ → ¬ ψ)
2 celaront.min . 2 x(χφ)
3 celaront.e . 2 xχ
41, 2, 3barbari 2305 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-1 5  ax-2 6  ax-3 7  ax-mp 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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