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Theorem disamis 2086
 Description: "Disamis", one of the syllogisms of Aristotelian logic. Some is , and all is , therefore some is . (In Aristotelian notation, IAI-3: MiP and MaS therefore SiP.) (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
disamis.maj
disamis.min
Assertion
Ref Expression
disamis

Proof of Theorem disamis
StepHypRef Expression
1 disamis.maj . 2
2 disamis.min . . . 4
32spi 1499 . . 3
43anim1i 336 . 2
51, 4eximii 1564 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1312  wex 1451 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  bocardo  2088
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