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Theorem dimatis 2014
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 1997 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 . . . . 5
32spi 1426 . . . 4
43adantl 262 . . 3
5 simpl 102 . . 3
64, 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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