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Theorem 0npi 6969
 Description: The empty set is not a positive integer. (Contributed by NM, 26-Aug-1995.)
Assertion
Ref Expression
0npi

Proof of Theorem 0npi
StepHypRef Expression
1 eqid 2095 . 2
2 elni 6964 . . . 4
32simprbi 270 . . 3
43necon2bi 2317 . 2
51, 4ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1296   wcel 1445   wne 2262  c0 3302  com 4433  cnpi 6928 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ne 2263  df-v 2635  df-dif 3015  df-sn 3472  df-ni 6960 This theorem is referenced by:  elni2  6970
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