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Theorem pnf0xnn0 8679
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 2085 . . 3 +∞ = +∞
21olci 684 . 2 (+∞ ∈ ℕ0 ∨ +∞ = +∞)
3 elxnn0 8674 . 2 (+∞ ∈ ℕ0* ↔ (+∞ ∈ ℕ0 ∨ +∞ = +∞))
42, 3mpbir 144 1 +∞ ∈ ℕ0*
Colors of variables: wff set class
Syntax hints:  wo 662   = wceq 1287  wcel 1436  +∞cpnf 7466  0cn0 8609  0*cxnn0 8672
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-13 1447  ax-14 1448  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-sep 3934  ax-pow 3986  ax-un 4236  ax-cnex 7383
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-pw 3417  df-sn 3437  df-pr 3438  df-uni 3639  df-pnf 7471  df-xr 7473  df-xnn0 8673
This theorem is referenced by:  inftonninf  9778
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