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Theorem celarent 2381
 Description: "Celarent", one of the syllogisms of Aristotelian logic. No is , and all is , therefore no is . (In Aristotelian notation, EAE-1: MeP and SaM therefore SeP.) For example, given the "No reptiles have fur" and "All snakes are reptiles", therefore "No snakes have fur". Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 24-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
celarent.maj
celarent.min
Assertion
Ref Expression
celarent

Proof of Theorem celarent
StepHypRef Expression
1 celarent.maj . 2
2 celarent.min . 2
31, 2barbara 2380 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567 This theorem depends on definitions:  df-bi 179  df-an 362
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