Theorem nn0xnn0 8650

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 8649	. 2 |- NN0 C_ NN0*
2	1	sseli 3008	1 |- ( A e. NN0 -> A e. NN0* )

Syntax hints:   -> wi 4   e. wcel 1436   NN0cn0 8583  NN0*cxnn0 8646

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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-un 2990  df-in 2992  df-ss 2999  df-xnn0 8647

This theorem is referenced by:  1tonninf  9749