Theorem nn0xnn0d 9219

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 9213	. 2 |- NN0 C_ NN0*
2		nn0xnn0d.1	. 2 |- ( ph -> A e. NN0 )
3	1, 2	sselid 3151	1 |- ( ph -> A e. NN0* )

Syntax hints:   -> wi 4   e. wcel 2146   NN0cn0 9147  NN0*cxnn0 9210

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 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-un 3131  df-in 3133  df-ss 3140  df-xnn0 9211

This theorem is referenced by:  pcxnn0cl  12275