Theorem 0xnn0 12598

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 12595	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12534	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3935	1 ⊢ 0 ∈ ℕ0*

This proof depends on syntax axioms:   ∈ wcel 2146  0cc0 11115  ℕ₀cn0 12519  ℕ₀^*cxnn0 12592

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-1cn 11173  ax-icn 11174  ax-addcl 11175  ax-mulcl 11177  ax-i2m1 11183

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-un 3911  df-ss 3923  df-sn 4592  df-n0 12520  df-xnn0 12593

This theorem is used by:  0edg0rgr  29980  rgrusgrprc  29997  rusgrprc  29998  rgrprcx  30000