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Theorem fresison 2416
Description: "Fresison", one of the syllogisms of Aristotelian logic. No is (PeM), and some is (MiS), therefore some is not (SoP). (In Aristotelian notation, EIO-4: PeM and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
fresison.maj
fresison.min
Assertion
Ref Expression
fresison

Proof of Theorem fresison
StepHypRef Expression
1 fresison.min . 2
2 simpr 461 . . 3
3 fresison.maj . . . . . 6
43spi 1864 . . . . 5
54con2i 120 . . . 4
65adantr 465 . . 3
72, 6jca 532 . 2
81, 7eximii 1658 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
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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