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 3912	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2119  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 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-1cn 11087  ax-icn 11088  ax-addcl 11089  ax-mulcl 11091  ax-i2m1 11097

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-un 3888  df-ss 3900  df-sn 4556  df-n0 12429  df-xnn0 12502

This theorem is referenced by:  0edg0rgr  29659  rgrusgrprc  29676  rusgrprc  29677  rgrprcx  29679