Theorem nn0ssxnn0 11366

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 3776	. 2 |- NN0 C_ ( NN0 u. { +oo } )
2		df-xnn0 11364	. 2 |- NN0* = ( NN0 u. { +oo } )
3	1, 2	sseqtr4i 3638	1 |- NN0 C_ NN0*

Syntax hints:   u. cun 3572   C_ wss 3574   {csn 4177   +oocpnf 10071   NN0cn0 11292  NN0*cxnn0 11363

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-in 3581  df-ss 3588  df-xnn0 11364

This theorem is referenced by:  nn0xnn0  11367  0xnn0  11369  nn0xnn0d  11372