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Theorem darapti 2413
 Description: "Darapti", one of the syllogisms of Aristotelian logic. All is , all is , and some exist, therefore some is . (In Aristotelian notation, AAI-3: MaP and MaS therefore SiP.) For example, "All squares are rectangles" and "All squares are rhombuses", therefore "Some rhombuses are rectangles". (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
darapti.maj
darapti.min
darapti.e
Assertion
Ref Expression
darapti

Proof of Theorem darapti
StepHypRef Expression
1 darapti.e . 2
2 darapti.min . . . 4
32spi 1865 . . 3
4 darapti.maj . . . 4
54spi 1865 . . 3
63, 5jca 532 . 2
71, 6eximii 1659 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wal 1393  wex 1613 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-12 1855 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614 This theorem is referenced by: (None)
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