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Theorem 0xnn0 9058
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 9055 . 2  |-  NN0  C_ NN0*
2 0nn0 9004 . 2  |-  0  e.  NN0
31, 2sselii 3094 1  |-  0  e. NN0*
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   0cc0 7632   NN0cn0 8989  NN0*cxnn0 9052
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-1cn 7725  ax-icn 7727  ax-addcl 7728  ax-mulcl 7730  ax-i2m1 7737
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-n0 8990  df-xnn0 9053
This theorem is referenced by:  0tonninf  10224
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