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Theorem celaront 2080
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 2079 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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