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Theorem cesare 2429
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 2424. (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 1767 . . 3
3 cesare.min . . . 4
43spi 1767 . . 3
52, 4nsyl3 114 . 2
65ax-gen 1562 1
Colors of variables: wff set class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1562  ax-4 1573  ax-5 1636  ax-6 1677  ax-7 1697  ax-12 1760
This theorem depends on definitions:  df-bi 179  df-ex 1558
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