Theorem 0xnn0 12521

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 12518	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12457	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3943	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2109  0cc0 11068  ℕ₀cn0 12442  ℕ₀^*cxnn0 12515

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 2701  ax-1cn 11126  ax-icn 11127  ax-addcl 11128  ax-mulcl 11130  ax-i2m1 11136

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 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-un 3919  df-ss 3931  df-sn 4590  df-n0 12443  df-xnn0 12516

This theorem is referenced by:  0edg0rgr  29500  rgrusgrprc  29517  rusgrprc  29518  rgrprcx  29520