Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  festino Unicode version

Theorem festino 2105
 Description: "Festino", one of the syllogisms of Aristotelian logic. No is , and some is , therefore some is not . (In Aristotelian notation, EIO-2: PeM and SiM therefore SoP.) (Contributed by David A. Wheeler, 25-Nov-2016.)
Hypotheses
Ref Expression
festino.maj
festino.min
Assertion
Ref Expression
festino

Proof of Theorem festino
StepHypRef Expression
1 festino.min . 2
2 festino.maj . . . . 5
32spi 1516 . . . 4
43con2i 616 . . 3
54anim2i 339 . 2
61, 5eximii 1581 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103  wal 1329  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514 This theorem depends on definitions:  df-bi 116 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator