Theorem nn0ssxnn0 9360

Description: The standard nonnegative integers are a subset of the extended nonnegative integers. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
nn0ssxnn0	|- NN0 C_ NN0*

Proof of Theorem nn0ssxnn0

Step	Hyp	Ref	Expression
1		ssun1 3335	. 2 |- NN0 C_ ( NN0 u. { +oo } )
2		df-xnn0 9358	. 2 |- NN0* = ( NN0 u. { +oo } )
3	1, 2	sseqtrri 3227	1 |- NN0 C_ NN0*

Syntax hints:   u. cun 3163   C_ wss 3165   {csn 3632   +oocpnf 8103   NN0cn0 9294  NN0*cxnn0 9357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-un 3169  df-in 3171  df-ss 3178  df-xnn0 9358

This theorem is referenced by:  nn0xnn0  9361  0xnn0  9363  nn0xnn0d  9366  nninfctlemfo  12332