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Theorem cesare 2402
Description: "Cesare", one of the syllogisms of Aristotelian logic. No is , and all is , therefore no is . (In Aristotelian notation, EAE-2: PeM and SaM therefore SeP.) Related to celarent 2397. (Contributed by David A. Wheeler, 27-Aug-2016.) (Revised by David A. Wheeler, 13-Nov-2016.)
Hypotheses
Ref Expression
cesare.maj
cesare.min
Assertion
Ref Expression
cesare

Proof of Theorem cesare
StepHypRef Expression
1 cesare.maj . . . 4
21spi 1864 . . 3
3 cesare.min . . . 4
43spi 1864 . . 3
52, 4nsyl3 119 . 2
65ax-gen 1618 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613
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