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Theorem ferio 2304
Description: "Ferio" ("Ferioque"), one of the syllogisms of Aristotelian logic. No φ is ψ, and some χ is φ, therefore some χ is not ψ. (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 x(φ → ¬ ψ)
ferio.min x(χ φ)
Assertion
Ref Expression
ferio x(χ ¬ ψ)

Proof of Theorem ferio
StepHypRef Expression
1 ferio.maj . 2 x(φ → ¬ ψ)
2 ferio.min . 2 x(χ φ)
31, 2darii 2303 1 x(χ ¬ ψ)
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-mp 5  ax-1 6  ax-2 7  ax-3 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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