Theorem 0xnn0 12516

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 12513	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12452	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3918	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2114  0cc0 11038  ℕ₀cn0 12437  ℕ₀^*cxnn0 12510

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708  ax-1cn 11096  ax-icn 11097  ax-addcl 11098  ax-mulcl 11100  ax-i2m1 11106

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-un 3894  df-ss 3906  df-sn 4568  df-n0 12438  df-xnn0 12511

This theorem is referenced by:  0edg0rgr  29641  rgrusgrprc  29658  rusgrprc  29659  rgrprcx  29661