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Theorem disamis 2314
 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 1753 . . . 4
43anim1i 551 . . 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:  bocardo  2316
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