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Theorem baroco 2400
Description: "Baroco", one of the syllogisms of Aristotelian logic. All  ph is  ps, and some  ch is not  ps, therefore some  ch is not  ph. (In Aristotelian notation, AOO-2: PaM and SoM therefore SoP.) For example, "All informative things are useful", "Some websites are not useful", therefore "Some websites are not informative." (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
baroco.maj  |-  A. x
( ph  ->  ps )
baroco.min  |-  E. x
( ch  /\  -.  ps )
Assertion
Ref Expression
baroco  |-  E. x
( ch  /\  -.  ph )

Proof of Theorem baroco
StepHypRef Expression
1 baroco.min . 2  |-  E. x
( ch  /\  -.  ps )
2 baroco.maj . . . . 5  |-  A. x
( ph  ->  ps )
32spi 1801 . . . 4  |-  ( ph  ->  ps )
43con3i 135 . . 3  |-  ( -. 
ps  ->  -.  ph )
54anim2i 569 . 2  |-  ( ( ch  /\  -.  ps )  ->  ( ch  /\  -.  ph ) )
61, 5eximii 1628 1  |-  E. x
( ch  /\  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 369   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by: (None)
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