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Theorem celaront 2003
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 2002 1  |-  E. x
( ch  /\  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 97   A.wal 1241   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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