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Theorem ferison 2254
Description: "Ferison", one of the syllogisms of Aristotelian logic. No  ph is  ps, and some  ph is  ch, therefore some  ch is not  ps. (In Aristotelian notation, EIO-3: MeP and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
ferison.maj  |-  A. x
( ph  ->  -.  ps )
ferison.min  |-  E. x
( ph  /\  ch )
Assertion
Ref Expression
ferison  |-  E. x
( ch  /\  -.  ps )

Proof of Theorem ferison
StepHypRef Expression
1 ferison.maj . 2  |-  A. x
( ph  ->  -.  ps )
2 ferison.min . 2  |-  E. x
( ph  /\  ch )
31, 2datisi 2252 1  |-  E. x
( ch  /\  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358   A.wal 1527   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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