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Theorem nn0xnn0 9273
Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
nn0xnn0  |-  ( A  e.  NN0  ->  A  e. NN0*
)

Proof of Theorem nn0xnn0
StepHypRef Expression
1 nn0ssxnn0 9272 . 2  |-  NN0  C_ NN0*
21sseli 3166 1  |-  ( A  e.  NN0  ->  A  e. NN0*
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2160   NN0cn0 9206  NN0*cxnn0 9269
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-xnn0 9270
This theorem is referenced by:  xnn0xadd0  9897  1tonninf  10471
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