Theorem 0xnn0 12471

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 12468	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12407	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3927	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2113  0cc0 11017  ℕ₀cn0 12392  ℕ₀^*cxnn0 12465

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-1cn 11075  ax-icn 11076  ax-addcl 11077  ax-mulcl 11079  ax-i2m1 11085

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-v 3439  df-un 3903  df-ss 3915  df-sn 4578  df-n0 12393  df-xnn0 12466

This theorem is referenced by:  0edg0rgr  29572  rgrusgrprc  29589  rusgrprc  29590  rgrprcx  29592