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Theorem ferio 2553
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 (Contributed by David A. Wheeler, 24-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Ref Expression
ferio.maj 𝑥(𝜑 → ¬ 𝜓)
ferio.min 𝑥(𝜒𝜑)
Ref Expression
ferio 𝑥(𝜒 ∧ ¬ 𝜓)

Proof of Theorem ferio
StepHypRef Expression
1 ferio.maj . 2 𝑥(𝜑 → ¬ 𝜓)
2 ferio.min . 2 𝑥(𝜒𝜑)
31, 2darii 2552 1 𝑥(𝜒 ∧ ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 382  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by: (None)
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