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Theorem disamis 2390
 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 1769 . . 3
43anim1i 552 . 2
51, 4eximii 1587 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550 This theorem is referenced by:  bocardo  2392 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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