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Theorem nnnn0i 8614
Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005.)
Hypothesis
Ref Expression
nnnn0.1  |-  N  e.  NN
Assertion
Ref Expression
nnnn0i  |-  N  e. 
NN0

Proof of Theorem nnnn0i
StepHypRef Expression
1 nnnn0.1 . 2  |-  N  e.  NN
2 nnnn0 8613 . 2  |-  ( N  e.  NN  ->  N  e.  NN0 )
31, 2ax-mp 7 1  |-  N  e. 
NN0
Colors of variables: wff set class
Syntax hints:    e. wcel 1436   NNcn 8357   NN0cn0 8606
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 2617  df-un 2992  df-in 2994  df-ss 3001  df-n0 8607
This theorem is referenced by:  1nn0  8622  2nn0  8623  3nn0  8624  4nn0  8625  5nn0  8626  6nn0  8627  7nn0  8628  8nn0  8629  9nn0  8630  numlt  8833  declei  8844  numlti  8845
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