Theorem nn0xnn0 9567

Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
nn0xnn0	|- ( A e. NN0 -> A e. NN0* )

Proof of Theorem nn0xnn0

Step	Hyp	Ref	Expression
1		nn0ssxnn0 9566	. 2 |- NN0 C_ NN0*
2	1	sseli 3234	1 |- ( A e. NN0 -> A e. NN0* )

Syntax hints:   -> wi 4   e. wcel 2203   NN0cn0 9496  NN0*cxnn0 9563

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-v 2815  df-un 3215  df-in 3217  df-ss 3224  df-xnn0 9564

This theorem is referenced by:  xnn0xadd0  10200  1tonninf  10803