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Theorem 0xnn0 12580
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 12577 . 2 0 ⊆ ℕ0*
2 0nn0 12517 . 2 0 ∈ ℕ0
31, 2sselii 3977 1 0 ∈ ℕ0*
Colors of variables: wff setvar class
Syntax hints:  wcel 2099  0cc0 11138  0cn0 12502  0*cxnn0 12574
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-1cn 11196  ax-icn 11197  ax-addcl 11198  ax-mulcl 11200  ax-i2m1 11206
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-un 3952  df-in 3954  df-ss 3964  df-sn 4630  df-n0 12503  df-xnn0 12575
This theorem is referenced by:  0edg0rgr  29385  rgrusgrprc  29402  rusgrprc  29403  rgrprcx  29405
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