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Theorem 0xnn0 11779
 Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
0xnn0 0 ∈ ℕ0*

Proof of Theorem 0xnn0
StepHypRef Expression
1 nn0ssxnn0 11776 . 2 0 ⊆ ℕ0*
2 0nn0 11718 . 2 0 ∈ ℕ0
31, 2sselii 3849 1 0 ∈ ℕ0*
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2050  0cc0 10329  ℕ0cn0 11701  ℕ0*cxnn0 11773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2744  ax-1cn 10387  ax-icn 10388  ax-addcl 10389  ax-mulcl 10391  ax-i2m1 10397 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-v 3411  df-un 3828  df-in 3830  df-ss 3837  df-sn 4436  df-n0 11702  df-xnn0 11774 This theorem is referenced by:  0edg0rgr  27051  rgrusgrprc  27068  rusgrprc  27069  rgrprcx  27071
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