Theorem 0xnn0 12578

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 12575	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 12514	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3934	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2143  0cc0 11095  ℕ₀cn0 12499  ℕ₀^*cxnn0 12572

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-1cn 11153  ax-icn 11154  ax-addcl 11155  ax-mulcl 11157  ax-i2m1 11163

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-un 3910  df-ss 3922  df-sn 4590  df-n0 12500  df-xnn0 12573

This theorem is referenced by:  0edg0rgr  29922  rgrusgrprc  29939  rusgrprc  29940  rgrprcx  29942