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Theorem darapti 2257
 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 . . . . 5
32spi 1738 . . . 4
4 darapti.maj . . . . 5
54spi 1738 . . . 4
63, 5jca 518 . . 3
76eximi 1563 . 2
81, 7ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1527  wex 1528 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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