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Theorem camestros 2389
 Description: "Camestros", one of the syllogisms of Aristotelian logic. All is , no is , and exist, therefore some is not . (In Aristotelian notation, AEO-2: PaM and SeM therefore SoP.) For example, "All horses have hooves", "No humans have hooves", and humans exist, therefore "Some humans are not horses". (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
camestros.maj
camestros.min
camestros.e
Assertion
Ref Expression
camestros

Proof of Theorem camestros
StepHypRef Expression
1 camestros.e . 2
2 camestros.min . . . . 5
32spi 1769 . . . 4
4 camestros.maj . . . . 5
54spi 1769 . . . 4
63, 5nsyl 115 . . 3
76ancli 535 . 2
81, 7eximii 1587 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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