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Theorem 0xnn0 11965
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 11962 . 2 0 ⊆ ℕ0*
2 0nn0 11904 . 2 0 ∈ ℕ0
31, 2sselii 3915 1 0 ∈ ℕ0*
Colors of variables: wff setvar class
Syntax hints:  wcel 2112  0cc0 10530  0cn0 11889  0*cxnn0 11959
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773  ax-1cn 10588  ax-icn 10589  ax-addcl 10590  ax-mulcl 10592  ax-i2m1 10598
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-sn 4529  df-n0 11890  df-xnn0 11960
This theorem is referenced by:  0edg0rgr  27366  rgrusgrprc  27383  rusgrprc  27384  rgrprcx  27386
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