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Theorem calemos 2118
 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 1516 . . . . 5
43con2i 616 . . . 4
5 calemos.maj . . . . 5
65spi 1516 . . . 4
74, 6nsyl 617 . . 3
87ancli 321 . 2
91, 8eximii 1581 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103  wal 1329  wex 1468 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 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514 This theorem depends on definitions:  df-bi 116 This theorem is referenced by: (None)
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