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Theorem nnnn0d 8011
Description: A positive integer is a nonnegative integer. (Contributed by Mario Carneiro, 27-May-2016.)
Hypothesis
Ref Expression
nnnn0d.1  NN
Assertion
Ref Expression
nnnn0d  NN0

Proof of Theorem nnnn0d
StepHypRef Expression
1 nnssnn0 7960 . 2  NN  C_  NN0
2 nnnn0d.1 . 2  NN
31, 2sseldi 2937 1  NN0
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   NNcn 7695   NN0cn0 7957
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-n0 7958
This theorem is referenced by:  nn0ge2m1nn0  8019  nnzd  8135  eluzge2nn0  8288  expinnval  8912  expgt1  8947  expaddzaplem  8952  expaddzap  8953  expmulzap  8955  expnbnd  9025
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