Theorem 0xnn0 12133

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 12130	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12070	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3884	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2112  0cc0 10694  ℕ₀cn0 12055  ℕ₀^*cxnn0 12127

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-8 2114  ax-9 2122  ax-ext 2708  ax-1cn 10752  ax-icn 10753  ax-addcl 10754  ax-mulcl 10756  ax-i2m1 10762

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2715  df-cleq 2728  df-clel 2809  df-v 3400  df-un 3858  df-in 3860  df-ss 3870  df-sn 4528  df-n0 12056  df-xnn0 12128

This theorem is referenced by:  0edg0rgr  27614  rgrusgrprc  27631  rusgrprc  27632  rgrprcx  27634