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Theorem camestros 2264
 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 . . . . . 6
32spi 1750 . . . . 5
4 camestros.maj . . . . . 6
54spi 1750 . . . . 5
63, 5nsyl 113 . . . 4
76ancli 534 . . 3
87eximi 1566 . 2
91, 8ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1530  wex 1531 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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