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Theorem disamis 2409
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 1864 . . 3
43anim1i 568 . 2
51, 4eximii 1658 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
This theorem is referenced by:  bocardo  2411
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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