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Theorem darii 2303
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 . . . . 5
32spi 1753 . . . 4
43anim2i 552 . . 3
54eximi 1576 . 2
61, 5ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  ferio  2304
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