Theorem 0xnn0 12546

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 12543	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12483	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3978	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2106  0cc0 11106  ℕ₀cn0 12468  ℕ₀^*cxnn0 12540

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-1cn 11164  ax-icn 11165  ax-addcl 11166  ax-mulcl 11168  ax-i2m1 11174

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-un 3952  df-in 3954  df-ss 3964  df-sn 4628  df-n0 12469  df-xnn0 12541

This theorem is referenced by:  0edg0rgr  28818  rgrusgrprc  28835  rusgrprc  28836  rgrprcx  28838