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Theorem 0npi 8761
 Description: The empty set is not a positive integer. (Contributed by NM, 26-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
0npi

Proof of Theorem 0npi
StepHypRef Expression
1 eqid 2438 . 2
2 elni 8755 . . . 4
32simprbi 452 . . 3
43necon2bi 2652 . 2
51, 4ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1653   wcel 1726   wne 2601  c0 3630  com 4847  cnpi 8721 This theorem is referenced by:  addasspi  8774  mulasspi  8776  distrpi  8777  addcanpi  8778  mulcanpi  8779  addnidpi  8780  ltapi  8782  ltmpi  8783  ordpipq  8821 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-sn 3822  df-ni 8751
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