Theorem 0xnn0 12549

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 12546	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12486	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3972	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2098  0cc0 11107  ℕ₀cn0 12471  ℕ₀^*cxnn0 12543

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-1cn 11165  ax-icn 11166  ax-addcl 11167  ax-mulcl 11169  ax-i2m1 11175

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3946  df-in 3948  df-ss 3958  df-sn 4622  df-n0 12472  df-xnn0 12544

This theorem is referenced by:  0edg0rgr  29323  rgrusgrprc  29340  rusgrprc  29341  rgrprcx  29343