Theorem nn0xnn0d 9073

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

Hypothesis

Ref	Expression
nn0xnn0d.1	|- ( ph -> A e. NN0 )

Assertion

Ref	Expression
nn0xnn0d	|- ( ph -> A e. NN0* )

Proof of Theorem nn0xnn0d

Step	Hyp	Ref	Expression
1		nn0ssxnn0 9067	. 2 |- NN0 C_ NN0*
2		nn0xnn0d.1	. 2 |- ( ph -> A e. NN0 )
3	1, 2	sseldi 3100	1 |- ( ph -> A e. NN0* )

Syntax hints:   -> wi 4   e. wcel 1481   NN0cn0 9001  NN0*cxnn0 9064

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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080  df-in 3082  df-ss 3089  df-xnn0 9065

This theorem is referenced by: (None)