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Theorem datisi 2052
Description: "Datisi", one of the syllogisms of Aristotelian logic. All  ph is  ps, and some  ph is  ch, therefore some  ch is  ps. (In Aristotelian notation, AII-3: MaP and MiS therefore SiP.) (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
datisi.maj  |-  A. x
( ph  ->  ps )
datisi.min  |-  E. x
( ph  /\  ch )
Assertion
Ref Expression
datisi  |-  E. x
( ch  /\  ps )

Proof of Theorem datisi
StepHypRef Expression
1 datisi.min . 2  |-  E. x
( ph  /\  ch )
2 simpr 108 . . 3  |-  ( (
ph  /\  ch )  ->  ch )
3 datisi.maj . . . . 5  |-  A. x
( ph  ->  ps )
43spi 1470 . . . 4  |-  ( ph  ->  ps )
54adantr 270 . . 3  |-  ( (
ph  /\  ch )  ->  ps )
62, 5jca 300 . 2  |-  ( (
ph  /\  ch )  ->  ( ch  /\  ps ) )
71, 6eximii 1534 1  |-  E. x
( ch  /\  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wal 1283   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ferison  2054
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