Theorem 0xnn0 12507

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 12504	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12443	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3919	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2114  0cc0 11029  ℕ₀cn0 12428  ℕ₀^*cxnn0 12501

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-1cn 11087  ax-icn 11088  ax-addcl 11089  ax-mulcl 11091  ax-i2m1 11097

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-un 3895  df-ss 3907  df-sn 4569  df-n0 12429  df-xnn0 12502

This theorem is referenced by:  0edg0rgr  29656  rgrusgrprc  29673  rusgrprc  29674  rgrprcx  29676