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Theorem nn0xnn0 8650
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 8649 . 2  |-  NN0  C_ NN0*
21sseli 3008 1  |-  ( A  e.  NN0  ->  A  e. NN0*
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1436   NN0cn0 8583  NN0*cxnn0 8646
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 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-un 2990  df-in 2992  df-ss 2999  df-xnn0 8647
This theorem is referenced by:  1tonninf  9749
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