Theorem 0xnn0 12611

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 12608	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12547	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3931	1 ⊢ 0 ∈ ℕ0*

This proof depends on syntax axioms:   ∈ wcel 2145  0cc0 11128  ℕ₀cn0 12532  ℕ₀^*cxnn0 12605

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 2147  ax-9 2155  ax-ext 2734  ax-1cn 11186  ax-icn 11187  ax-addcl 11188  ax-mulcl 11190  ax-i2m1 11196

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 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-un 3907  df-ss 3919  df-sn 4588  df-n0 12533  df-xnn0 12606

This theorem is used by:  0edg0rgr  30040  rgrusgrprc  30057  rusgrprc  30058  rgrprcx  30060