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Theorem ferio 2380
 Description: "Ferio" ("Ferioque"), one of the syllogisms of Aristotelian logic. No is , and some is , therefore some is not . (In Aristotelian notation, EIO-1: MeP and SiM therefore SoP.) For example, given "No homework is fun" and "Some reading is homework", therefore "Some reading is not fun". This is essentially a logical axiom in Aristotelian logic. Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 24-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
ferio.maj
ferio.min
Assertion
Ref Expression
ferio

Proof of Theorem ferio
StepHypRef Expression
1 ferio.maj . 2
2 ferio.min . 2
31, 2darii 2379 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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