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Theorem camestros 2109
 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 1517 . . . 4
4 camestros.maj . . . . 5
54spi 1517 . . . 4
63, 5nsyl 618 . . 3
76ancli 321 . 2
81, 7eximii 1582 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103  wal 1330  wex 1469 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515 This theorem depends on definitions:  df-bi 116 This theorem is referenced by: (None)
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