Theorem 0xnn0 12554

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 12551	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12490	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3931	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2141  0cc0 11067  ℕ₀cn0 12475  ℕ₀^*cxnn0 12548

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-1cn 11125  ax-icn 11126  ax-addcl 11127  ax-mulcl 11129  ax-i2m1 11135

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-un 3907  df-ss 3919  df-sn 4580  df-n0 12476  df-xnn0 12549

This theorem is referenced by:  0edg0rgr  29730  rgrusgrprc  29747  rusgrprc  29748  rgrprcx  29750