Theorem nnnn0i 8433

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

Step	Hyp	Ref	Expression
1		nnnn0.1	. 2 |- N e. NN
2		nnnn0 8432	. 2 |- ( N e. NN -> N e. NN0 )
3	1, 2	ax-mp 7	1 |- N e. NN0

Syntax hints:   e. wcel 1434   NNcn 8176   NN0cn0 8425

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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-n0 8426

This theorem is referenced by:  1nn0  8441  2nn0  8442  3nn0  8443  4nn0  8444  5nn0  8445  6nn0  8446  7nn0  8447  8nn0  8448  9nn0  8449  numlt  8652  declei  8663  numlti  8664