Theorem 0xnn0 12633

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 12630	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12570	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 4005	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2108  0cc0 11186  ℕ₀cn0 12555  ℕ₀^*cxnn0 12627

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-1cn 11244  ax-icn 11245  ax-addcl 11246  ax-mulcl 11248  ax-i2m1 11254

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-un 3981  df-ss 3993  df-sn 4649  df-n0 12556  df-xnn0 12628

This theorem is referenced by:  0edg0rgr  29610  rgrusgrprc  29627  rusgrprc  29628  rgrprcx  29630