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Theorem nnssnn0 8242
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 3134 . 2  |-  NN  C_  ( NN  u.  { 0 } )
2 df-n0 8240 . 2  |-  NN0  =  ( NN  u.  { 0 } )
31, 2sseqtr4i 3006 1  |-  NN  C_  NN0
Colors of variables: wff set class
Syntax hints:    u. cun 2943    C_ wss 2945   {csn 3403   0cc0 6947   NNcn 7990   NN0cn0 8239
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-n0 8240
This theorem is referenced by:  nnnn0  8246  nnnn0d  8292  oddge22np1  10193
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