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Theorem nnnn0i 9008
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 9007 . 2  |-  ( N  e.  NN  ->  N  e.  NN0 )
31, 2ax-mp 5 1  |-  N  e. 
NN0
Colors of variables: wff set class
Syntax hints:    e. wcel 1481   NNcn 8743   NN0cn0 9000
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-n0 9001
This theorem is referenced by:  1nn0  9016  2nn0  9017  3nn0  9018  4nn0  9019  5nn0  9020  6nn0  9021  7nn0  9022  8nn0  9023  9nn0  9024  numlt  9229  declei  9240  numlti  9241
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