Theorem 0xnn0 11582

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 11579	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 11520	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3742	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2140  0cc0 10149  ℕ₀cn0 11505  ℕ₀^*cxnn0 11576

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741  ax-1cn 10207  ax-icn 10208  ax-addcl 10209  ax-mulcl 10211  ax-i2m1 10217

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-v 3343  df-un 3721  df-in 3723  df-ss 3730  df-sn 4323  df-n0 11506  df-xnn0 11577

This theorem is referenced by:  0edg0rgr  26700  rgrusgrprc  26717  rusgrprc  26718  rgrprcx  26720