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Theorem calemes 2414
Description: "Calemes", one of the syllogisms of Aristotelian logic. All is , and no is , therefore no is . (In Aristotelian notation, AEE-4: PaM and MeS therefore SeP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
calemes.maj
calemes.min
Assertion
Ref Expression
calemes

Proof of Theorem calemes
StepHypRef Expression
1 calemes.min . . . . 5
21spi 1864 . . . 4
32con2i 120 . . 3
4 calemes.maj . . . 4
54spi 1864 . . 3
63, 5nsyl 121 . 2
76ax-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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