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Theorem celaront 2383
Description: "Celaront", one of the syllogisms of Aristotelian logic. No  ph is  ps, all  ch is  ph, and some  ch exist, therefore some  ch is not  ps. (In Aristotelian notation, EAO-1: MeP and SaM therefore SoP.) For example, given "No reptiles have fur", "All snakes are reptiles.", and "Snakes exist.", prove "Some snakes have no fur". Note the existence hypothesis. Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 27-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
celaront.maj  |-  A. x
( ph  ->  -.  ps )
celaront.min  |-  A. x
( ch  ->  ph )
celaront.e  |-  E. x ch
Assertion
Ref Expression
celaront  |-  E. x
( ch  /\  -.  ps )

Proof of Theorem celaront
StepHypRef Expression
1 celaront.maj . 2  |-  A. x
( ph  ->  -.  ps )
2 celaront.min . 2  |-  A. x
( ch  ->  ph )
3 celaront.e . 2  |-  E. x ch
41, 2, 3barbari 2382 1  |-  E. x
( ch  /\  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 359   A.wal 1549   E.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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