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Theorem darii 2382
 Description: "Darii", one of the syllogisms of Aristotelian logic. All is , and some is , therefore some is . (In Aristotelian notation, AII-1: MaP and SiM therefore SiP.) For example, given "All rabbits have fur" and "Some pets are rabbits", therefore "Some pets have fur". Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 24-Aug-2016.)
Hypotheses
Ref Expression
darii.maj
darii.min
Assertion
Ref Expression
darii

Proof of Theorem darii
StepHypRef Expression
1 darii.min . 2
2 darii.maj . . . 4
32spi 1770 . . 3
43anim2i 554 . 2
51, 4eximii 1588 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550  wex 1551 This theorem is referenced by:  ferio  2383 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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