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Theorem calemes 2396
 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 1769 . . . 4
32con2i 114 . . 3
4 calemes.maj . . . 4
54spi 1769 . . 3
63, 5nsyl 115 . 2
76ax-gen 1555 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-ex 1551
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