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Theorem camestres 2308
 Description: "Camestres", one of the syllogisms of Aristotelian logic. All φ is ψ, and no χ is ψ, therefore no χ is φ. (In Aristotelian notation, AEE-2: PaM and SeM therefore SeP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
camestres.maj x(φψ)
camestres.min x(χ → ¬ ψ)
Assertion
Ref Expression
camestres x(χ → ¬ φ)

Proof of Theorem camestres
StepHypRef Expression
1 camestres.min . . . 4 x(χ → ¬ ψ)
21spi 1753 . . 3 (χ → ¬ ψ)
3 camestres.maj . . . 4 x(φψ)
43spi 1753 . . 3 (φψ)
52, 4nsyl 113 . 2 (χ → ¬ φ)
65ax-gen 1546 1 x(χ → ¬ φ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540 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-ex 1542 This theorem is referenced by: (None)
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