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Theorem camestres 2348
Description: "Camestres", one of the syllogisms of Aristotelian logic. All  ph is  ps, and no  ch is  ps, therefore no  ch is  ph. (In Aristotelian notation, AEE-2: PaM and SeM therefore SeP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
camestres.maj  |-  A. x
( ph  ->  ps )
camestres.min  |-  A. x
( ch  ->  -.  ps )
Assertion
Ref Expression
camestres  |-  A. x
( ch  ->  -.  ph )

Proof of Theorem camestres
StepHypRef Expression
1 camestres.min . . . 4  |-  A. x
( ch  ->  -.  ps )
21spi 1888 . . 3  |-  ( ch 
->  -.  ps )
3 camestres.maj . . . 4  |-  A. x
( ph  ->  ps )
43spi 1888 . . 3  |-  ( ph  ->  ps )
52, 4nsyl 121 . 2  |-  ( ch 
->  -.  ph )
65ax-gen 1639 1  |-  A. x
( ch  ->  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-12 1878
This theorem depends on definitions:  df-bi 185  df-ex 1634
This theorem is referenced by: (None)
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