Theorem 0xnn0 12455

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 12452	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12391	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3926	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2111  0cc0 11001  ℕ₀cn0 12376  ℕ₀^*cxnn0 12449

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-1cn 11059  ax-icn 11060  ax-addcl 11061  ax-mulcl 11063  ax-i2m1 11069

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-un 3902  df-ss 3914  df-sn 4572  df-n0 12377  df-xnn0 12450

This theorem is referenced by:  0edg0rgr  29546  rgrusgrprc  29563  rusgrprc  29564  rgrprcx  29566