Theorem 0xnn0 12725

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 12722	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12661	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3910	1 ⊢ 0 ∈ ℕ0*

This proof depends on syntax axioms:   ∈ wcel 2147  0cc0 11239  ℕ₀cn0 12646  ℕ₀^*cxnn0 12719

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-1cn 11297  ax-icn 11298  ax-addcl 11299  ax-mulcl 11301  ax-i2m1 11307

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154  df-sn 4589  df-n0 12647  df-xnn0 12720

This theorem is used by:  0edg0rgr  30210  rgrusgrprc  30227  rusgrprc  30228  rgrprcx  30230