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Theorem disamis 2266
 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 . . . . 5
32spi 1750 . . . 4
43anim1i 551 . . 3
54eximi 1566 . 2
61, 5ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1530  wex 1531 This theorem is referenced by:  bocardo  2268 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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