Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dimatis Structured version   Unicode version

Theorem dimatis 2415
 Description: "Dimatis", one of the syllogisms of Aristotelian logic. Some is , and all is , therefore some is . (In Aristotelian notation, IAI-4: PiM and MaS therefore SiP.) For example, "Some pets are rabbits.", "All rabbits have fur", therefore "Some fur bearing animals are pets". Like darii 2398 with positions interchanged. (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
dimatis.maj
dimatis.min
Assertion
Ref Expression
dimatis

Proof of Theorem dimatis
StepHypRef Expression
1 dimatis.maj . 2
2 dimatis.min . . . . 5
32spi 1865 . . . 4
5 simpl 457 . . 3
64, 5jca 532 . 2
71, 6eximii 1659 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wal 1393  wex 1613 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-12 1855 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator