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Theorem baroco 2405
Description: "Baroco", one of the syllogisms of Aristotelian logic. All is , and some is not , therefore some is not . (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
baroco.min
Assertion
Ref Expression
baroco

Proof of Theorem baroco
StepHypRef Expression
1 baroco.min . 2
2 baroco.maj . . . . 5
32spi 1864 . . . 4
43con3i 135 . . 3
54anim2i 569 . 2
61, 5eximii 1658 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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