Theorem nn0xnn0 9202

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 9201	. 2 |- NN0 C_ NN0*
2	1	sseli 3143	1 |- ( A e. NN0 -> A e. NN0* )

Syntax hints:   -> wi 4   e. wcel 2141   NN0cn0 9135  NN0*cxnn0 9198

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-xnn0 9199

This theorem is referenced by:  xnn0xadd0  9824  1tonninf  10396