Theorem nn0xnn0d 9639

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 9633	. 2 |- NN0 C_ NN0*
2		nn0xnn0d.1	. 2 |- ( ph -> A e. NN0 )
3	1, 2	sselid 3246	1 |- ( ph -> A e. NN0* )

This proof depends on syntax axioms:   -> wi 4   e. wcel 2209   NN0cn0 9563  NN0*cxnn0 9630

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-xnn0 9631

This theorem is used by:  pcxnn0cl  13089