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Theorem xnn0nnn0pnf 8641
 Description: An extended nonnegative integer which is not a standard nonnegative integer is positive infinity. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
xnn0nnn0pnf NN0*

Proof of Theorem xnn0nnn0pnf
StepHypRef Expression
1 elxnn0 8630 . . 3 NN0*
2 pm2.53 674 . . 3
31, 2sylbi 119 . 2 NN0*
43imp 122 1 NN0*
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 102   wo 662   wceq 1285   wcel 1434   cpnf 7420  cn0 8563  NN0*cxnn0 8626 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3922  ax-pow 3974  ax-un 4223  ax-cnex 7337 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-v 2614  df-un 2988  df-in 2990  df-ss 2997  df-pw 3408  df-sn 3428  df-pr 3429  df-uni 3628  df-pnf 7425  df-xr 7427  df-xnn0 8628 This theorem is referenced by: (None)
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