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Theorem felapton 2393
 Description: "Felapton", one of the syllogisms of Aristotelian logic. No is , all is , and some exist, therefore some is not . (In Aristotelian notation, EAO-3: MeP and MaS therefore SoP.) For example, "No flowers are animals" and "All flowers are plants", therefore "Some plants are not animals". (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
felapton.maj
felapton.min
felapton.e
Assertion
Ref Expression
felapton

Proof of Theorem felapton
StepHypRef Expression
1 felapton.e . 2
2 felapton.min . . . 4
32spi 1769 . . 3
4 felapton.maj . . . 4
54spi 1769 . . 3
63, 5jca 519 . 2
71, 6eximii 1587 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550 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-an 361  df-ex 1551
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