Theorem nn0xnn0d 9321

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 9315	. 2 |- NN0 C_ NN0*
2		nn0xnn0d.1	. 2 |- ( ph -> A e. NN0 )
3	1, 2	sselid 3181	1 |- ( ph -> A e. NN0* )

Syntax hints:   -> wi 4   e. wcel 2167   NN0cn0 9249  NN0*cxnn0 9312

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-in 3163  df-ss 3170  df-xnn0 9313

This theorem is referenced by:  pcxnn0cl  12479