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Theorem ferio 2078
Description: "Ferio" ("Ferioque"), one of the syllogisms of Aristotelian logic. No  ph is  ps, and some  ch is  ph, therefore some  ch is not  ps. (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  |-  A. x
( ph  ->  -.  ps )
ferio.min  |-  E. x
( ch  /\  ph )
Assertion
Ref Expression
ferio  |-  E. x
( ch  /\  -.  ps )

Proof of Theorem ferio
StepHypRef Expression
1 ferio.maj . 2  |-  A. x
( ph  ->  -.  ps )
2 ferio.min . 2  |-  E. x
( ch  /\  ph )
31, 2darii 2077 1  |-  E. x
( ch  /\  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103   A.wal 1314   E.wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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