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Theorem nnssnn0 9174
Description: Positive naturals are a subset of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002.)
Assertion
Ref Expression
nnssnn0  |-  NN  C_  NN0

Proof of Theorem nnssnn0
StepHypRef Expression
1 ssun1 3298 . 2  |-  NN  C_  ( NN  u.  { 0 } )
2 df-n0 9172 . 2  |-  NN0  =  ( NN  u.  { 0 } )
31, 2sseqtrri 3190 1  |-  NN  C_  NN0
Colors of variables: wff set class
Syntax hints:    u. cun 3127    C_ wss 3129   {csn 3592   0cc0 7807   NNcn 8914   NN0cn0 9171
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-n0 9172
This theorem is referenced by:  nnnn0  9178  nnnn0d  9224  expcnv  11504  oddge22np1  11877
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