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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 1864 . . 3
4 darapti.maj . . . 4
54spi 1864 . . 3
63, 5jca 532 . 2
71, 6eximii 1658 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
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-an 371  df-ex 1613
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