Theorem 0xnn0 12588

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 12585	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12524	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3960	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2107  0cc0 11137  ℕ₀cn0 12509  ℕ₀^*cxnn0 12582

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706  ax-1cn 11195  ax-icn 11196  ax-addcl 11197  ax-mulcl 11199  ax-i2m1 11205

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3465  df-un 3936  df-ss 3948  df-sn 4607  df-n0 12510  df-xnn0 12583

This theorem is referenced by:  0edg0rgr  29518  rgrusgrprc  29535  rusgrprc  29536  rgrprcx  29538