Theorem 0xnn0 12612

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 12609	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12548	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3995	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2108  0cc0 11162  ℕ₀cn0 12533  ℕ₀^*cxnn0 12606

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 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11220  ax-icn 11221  ax-addcl 11222  ax-mulcl 11224  ax-i2m1 11230

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1542  df-ex 1779  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3483  df-un 3971  df-ss 3983  df-sn 4635  df-n0 12534  df-xnn0 12607

This theorem is referenced by:  0edg0rgr  29616  rgrusgrprc  29633  rusgrprc  29634  rgrprcx  29636