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Theorem pnf0xnn0 11784
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 2771 . . 3 +∞ = +∞
21olci 853 . 2 (+∞ ∈ ℕ0 ∨ +∞ = +∞)
3 elxnn0 11779 . 2 (+∞ ∈ ℕ0* ↔ (+∞ ∈ ℕ0 ∨ +∞ = +∞))
42, 3mpbir 223 1 +∞ ∈ ℕ0*
Colors of variables: wff setvar class
Syntax hints:  wo 834   = wceq 1508  wcel 2051  +∞cpnf 10469  0cn0 11705  0*cxnn0 11777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929  ax-7 1966  ax-8 2053  ax-9 2060  ax-10 2080  ax-11 2094  ax-12 2107  ax-ext 2743  ax-sep 5056  ax-pow 5115  ax-un 7277  ax-cnex 10389
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 835  df-tru 1511  df-ex 1744  df-nf 1748  df-sb 2017  df-clab 2752  df-cleq 2764  df-clel 2839  df-nfc 2911  df-rex 3087  df-v 3410  df-un 3827  df-in 3829  df-ss 3836  df-pw 4418  df-sn 4436  df-uni 4709  df-pnf 10474  df-xnn0 11778
This theorem is referenced by:  xnn0xaddcl  12443
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