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Theorem 0xnn0 8742
Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
0xnn0  |-  0  e. NN0*

Proof of Theorem 0xnn0
StepHypRef Expression
1 nn0ssxnn0 8739 . 2  |-  NN0  C_ NN0*
2 0nn0 8688 . 2  |-  0  e.  NN0
31, 2sselii 3022 1  |-  0  e. NN0*
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   0cc0 7350   NN0cn0 8673  NN0*cxnn0 8736
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-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-1cn 7438  ax-icn 7440  ax-addcl 7441  ax-mulcl 7443  ax-i2m1 7450
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-sn 3452  df-n0 8674  df-xnn0 8737
This theorem is referenced by:  0tonninf  9845
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