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Theorem fresison 2321
 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 447 . . . 4
3 fresison.maj . . . . . . 7
43spi 1753 . . . . . 6
54con2i 112 . . . . 5
65adantr 451 . . . 4
72, 6jca 518 . . 3
87eximi 1576 . 2
91, 8ax-mp 8 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540  wex 1541 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by: (None)
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