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Theorem calemes 2441
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 1767 . . . 4
32con2i 115 . . 3
4 calemes.maj . . . 4
54spi 1767 . . 3
63, 5nsyl 116 . 2
76ax-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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