Theorem 0xnn0 12241

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 12238	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12178	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3914	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2108  0cc0 10802  ℕ₀cn0 12163  ℕ₀^*cxnn0 12235

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-1cn 10860  ax-icn 10861  ax-addcl 10862  ax-mulcl 10864  ax-i2m1 10870

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-un 3888  df-in 3890  df-ss 3900  df-sn 4559  df-n0 12164  df-xnn0 12236

This theorem is referenced by:  0edg0rgr  27842  rgrusgrprc  27859  rusgrprc  27860  rgrprcx  27862