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Theorem datisi 2110
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 109 . . 3  |-  ( (
ph  /\  ch )  ->  ch )
3 datisi.maj . . . . 5  |-  A. x
( ph  ->  ps )
43spi 1517 . . . 4  |-  ( ph  ->  ps )
54adantr 274 . . 3  |-  ( (
ph  /\  ch )  ->  ps )
62, 5jca 304 . 2  |-  ( (
ph  /\  ch )  ->  ( ch  /\  ps ) )
71, 6eximii 1582 1  |-  E. x
( ch  /\  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   A.wal 1330   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ferison  2112
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