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Theorem pnf0xnn0 8495
 Description: Positive infinity is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
pnf0xnn0 +∞ ∈ ℕ0*

Proof of Theorem pnf0xnn0
StepHypRef Expression
1 eqid 2083 . . 3 +∞ = +∞
21olci 684 . 2 (+∞ ∈ ℕ0 ∨ +∞ = +∞)
3 elxnn0 8490 . 2 (+∞ ∈ ℕ0* ↔ (+∞ ∈ ℕ0 ∨ +∞ = +∞))
42, 3mpbir 144 1 +∞ ∈ ℕ0*
 Colors of variables: wff set class Syntax hints:   ∨ wo 662   = wceq 1285   ∈ wcel 1434  +∞cpnf 7282  ℕ0cn0 8425  ℕ0*cxnn0 8488 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3916  ax-pow 3968  ax-un 4216  ax-cnex 7199 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-pw 3402  df-sn 3422  df-pr 3423  df-uni 3622  df-pnf 7287  df-xr 7289  df-xnn0 8489 This theorem is referenced by: (None)
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