Theorem 0xnn0 12528

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 12525	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12464	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3946	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2109  0cc0 11075  ℕ₀cn0 12449  ℕ₀^*cxnn0 12522

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702  ax-1cn 11133  ax-icn 11134  ax-addcl 11135  ax-mulcl 11137  ax-i2m1 11143

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-un 3922  df-ss 3934  df-sn 4593  df-n0 12450  df-xnn0 12523

This theorem is referenced by:  0edg0rgr  29507  rgrusgrprc  29524  rusgrprc  29525  rgrprcx  29527