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Theorem calemos 2420
 Description: "Calemos", one of the syllogisms of Aristotelian logic. All is (PaM), no is (MeS), and exist, therefore some is not (SoP). (In Aristotelian notation, AEO-4: PaM and MeS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
calemos.maj
calemos.min
calemos.e
Assertion
Ref Expression
calemos

Proof of Theorem calemos
StepHypRef Expression
1 calemos.e . 2
2 calemos.min . . . . . 6
32spi 1808 . . . . 5
43con2i 120 . . . 4
5 calemos.maj . . . . 5
65spi 1808 . . . 4
74, 6nsyl 121 . . 3
87ancli 551 . 2
91, 8eximii 1632 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369  wal 1372  wex 1591 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-12 1798 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592 This theorem is referenced by: (None)
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