Theorem nnnn0i 8837

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 8836	. 2 |- ( N e. NN -> N e. NN0 )
3	1, 2	ax-mp 7	1 |- N e. NN0

Syntax hints:   e. wcel 1448   NNcn 8578   NN0cn0 8829

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082

This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-n0 8830

This theorem is referenced by:  1nn0  8845  2nn0  8846  3nn0  8847  4nn0  8848  5nn0  8849  6nn0  8850  7nn0  8851  8nn0  8852  9nn0  8853  numlt  9058  declei  9069  numlti  9070