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Theorem baroco 2007
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 1429 . . . 4  |-  ( ph  ->  ps )
43con3i 562 . . 3  |-  ( -. 
ps  ->  -.  ph )
54anim2i 324 . 2  |-  ( ( ch  /\  -.  ps )  ->  ( ch  /\  -.  ph ) )
61, 5eximii 1493 1  |-  E. x
( ch  /\  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 97   A.wal 1241   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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