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Theorem dimatis 2272
 Description: "Dimatis", one of the syllogisms of Aristotelian logic. Some is , and all is , therefore some is . (In Aristotelian notation, IAI-4: PiM and MaS therefore SiP.) For example, "Some pets are rabbits.", "All rabbits have fur", therefore "Some fur bearing animals are pets". Like darii 2255 with positions interchanged. (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
dimatis.maj
dimatis.min
Assertion
Ref Expression
dimatis

Proof of Theorem dimatis
StepHypRef Expression
1 dimatis.maj . 2
2 dimatis.min . . . . . 6
32spi 1750 . . . . 5
43adantl 452 . . . 4
5 simpl 443 . . . 4
64, 5jca 518 . . 3
76eximi 1566 . 2
81, 7ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1530  wex 1531 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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