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Theorem nnssnn0 10226
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 3512 . 2  |-  NN  C_  ( NN  u.  { 0 } )
2 df-n0 10224 . 2  |-  NN0  =  ( NN  u.  { 0 } )
31, 2sseqtr4i 3383 1  |-  NN  C_  NN0
Colors of variables: wff set class
Syntax hints:    u. cun 3320    C_ wss 3322   {csn 3816   0cc0 8992   NNcn 10002   NN0cn0 10223
This theorem is referenced by:  nnnn0  10230  nnnn0d  10276  nthruz  12853  bitsfzolem  12948  ramub1  13398  ramcl  13399  ply1divex  20061  pserdvlem2  20346  hbtlem5  27311
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-n0 10224
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