Theorem 0xnn0 12545

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 12542	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12482	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3977	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2107  0cc0 11105  ℕ₀cn0 12467  ℕ₀^*cxnn0 12539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-1cn 11163  ax-icn 11164  ax-addcl 11165  ax-mulcl 11167  ax-i2m1 11173

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3951  df-in 3953  df-ss 3963  df-sn 4627  df-n0 12468  df-xnn0 12540

This theorem is referenced by:  0edg0rgr  28808  rgrusgrprc  28825  rusgrprc  28826  rgrprcx  28828