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Theorem 0npi 9281
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 2457 . 2
2 elni 9275 . . . 4
32simprbi 464 . . 3
43necon2bi 2694 . 2
51, 4ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  =wceq 1395  e.wcel 1818  =/=wne 2652   c0 3784   com 6700   cnpi 9243
This theorem is referenced by:  addasspi  9294  mulasspi  9296  distrpi  9297  addcanpi  9298  mulcanpi  9299  addnidpi  9300  ltapi  9302  ltmpi  9303  ordpipq  9341
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-sn 4030  df-ni 9271
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