Theorem 0xnn0 9263

Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
0xnn0	⊢ 0 ∈ ℕ0*

Proof of Theorem 0xnn0

Step	Hyp	Ref	Expression
1		nn0ssxnn0 9260	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 9209	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3167	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2160  0cc0 7829  ℕ₀cn0 9194  ℕ₀^*cxnn0 9257

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-1cn 7922  ax-icn 7924  ax-addcl 7925  ax-mulcl 7927  ax-i2m1 7934

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-n0 9195  df-xnn0 9258

This theorem is referenced by:  0tonninf  10457