Theorem 0xnn0 12311

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 12308	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12248	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3918	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2106  0cc0 10871  ℕ₀cn0 12233  ℕ₀^*cxnn0 12305

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-1cn 10929  ax-icn 10930  ax-addcl 10931  ax-mulcl 10933  ax-i2m1 10939

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-un 3892  df-in 3894  df-ss 3904  df-sn 4562  df-n0 12234  df-xnn0 12306

This theorem is referenced by:  0edg0rgr  27939  rgrusgrprc  27956  rusgrprc  27957  rgrprcx  27959