Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  calemos Unicode version

Theorem calemos 2261
 Description: "Calemos", one of the syllogisms of Aristotelian logic. All is (PaM), no is (MeS), and exist, therefore some is not (SoP). (In Aristotelian notation, AEO-4: PaM and MeS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)
Hypotheses
Ref Expression
calemos.maj
calemos.min
calemos.e
Assertion
Ref Expression
calemos

Proof of Theorem calemos
StepHypRef Expression
1 calemos.e . 2
2 calemos.min . . . . . . 7
32spi 1738 . . . . . 6
43con2i 112 . . . . 5
5 calemos.maj . . . . . 6
65spi 1738 . . . . 5
74, 6nsyl 113 . . . 4
87ancli 534 . . 3
98eximi 1563 . 2
101, 9ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1527  wex 1528 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
 Copyright terms: Public domain W3C validator