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Theorem disamis 2253
Description: "Disamis", one of the syllogisms of Aristotelian logic. Some  ph is  ps, and all  ph is  ch, therefore some  ch is  ps. (In Aristotelian notation, IAI-3: MiP and MaS therefore SiP.) (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
disamis.maj  |-  E. x
( ph  /\  ps )
disamis.min  |-  A. x
( ph  ->  ch )
Assertion
Ref Expression
disamis  |-  E. x
( ch  /\  ps )

Proof of Theorem disamis
StepHypRef Expression
1 disamis.maj . 2  |-  E. x
( ph  /\  ps )
2 disamis.min . . . . 5  |-  A. x
( ph  ->  ch )
32spi 1738 . . . 4  |-  ( ph  ->  ch )
43anim1i 551 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  /\  ps ) )
54eximi 1563 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x
( ch  /\  ps ) )
61, 5ax-mp 8 1  |-  E. x
( ch  /\  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1527   E.wex 1528
This theorem is referenced by:  bocardo  2255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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