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Theorem fesapo 2328
 Description: "Fesapo", one of the syllogisms of Aristotelian logic. No is , all is , and exist, therefore some is not . (In Aristotelian notation, EAO-4: PeM and MaS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
fesapo.maj
fesapo.min
fesapo.e
Assertion
Ref Expression
fesapo

Proof of Theorem fesapo
StepHypRef Expression
1 fesapo.e . 2
2 fesapo.min . . . . 5
32spi 1754 . . . 4
4 fesapo.maj . . . . . 6
54spi 1754 . . . . 5
65con2i 112 . . . 4
73, 6jca 518 . . 3
87eximi 1576 . 2
91, 8ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1540  wex 1541 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
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