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Theorem darapti 2012
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 1426 . . 3
4 darapti.maj . . . 4
54spi 1426 . . 3
63, 5jca 290 . 2
71, 6eximii 1490 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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