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Theorem darii 2043
 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 1470 . . 3
43anim2i 334 . 2
51, 4eximii 1534 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wal 1283  wex 1422 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468 This theorem depends on definitions:  df-bi 115 This theorem is referenced by:  ferio  2044
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