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Theorem cesaro 2389
 Description: "Cesaro", one of the syllogisms of Aristotelian logic. No is , all is , and exist, therefore some is not . (In Aristotelian notation, EAO-2: PeM and SaM therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
cesaro.maj
cesaro.min
cesaro.e
Assertion
Ref Expression
cesaro

Proof of Theorem cesaro
StepHypRef Expression
1 cesaro.e . 2
2 cesaro.maj . . . . 5
32spi 1770 . . . 4
4 cesaro.min . . . . 5
54spi 1770 . . . 4
63, 5nsyl3 114 . . 3
76ancli 536 . 2
81, 7eximii 1588 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wal 1550  wex 1551 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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