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Theorem bocardo 2395
 Description: "Bocardo", one of the syllogisms of Aristotelian logic. Some is not , and all is , therefore some is not . (In Aristotelian notation, OAO-3: MoP and MaS therefore SoP.) For example, "Some cats have no tails", "All cats are mammals", therefore "Some mammals have no tails". A reorder of disamis 2393; prefer using that instead. (Contributed by David A. Wheeler, 28-Aug-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
bocardo.maj
bocardo.min
Assertion
Ref Expression
bocardo

Proof of Theorem bocardo
StepHypRef Expression
1 bocardo.maj . 2
2 bocardo.min . 2
31, 2disamis 2393 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wal 1550  wex 1551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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