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Theorem pnf0xnn0 8713
Description: Positive infinity is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
pnf0xnn0  |- +oo  e. NN0*

Proof of Theorem pnf0xnn0
StepHypRef Expression
1 eqid 2088 . . 3  |- +oo  = +oo
21olci 686 . 2  |-  ( +oo  e.  NN0  \/ +oo  = +oo )
3 elxnn0 8708 . 2  |-  ( +oo  e. NN0*  <-> 
( +oo  e.  NN0  \/ +oo  = +oo )
)
42, 3mpbir 144 1  |- +oo  e. NN0*
Colors of variables: wff set class
Syntax hints:    \/ wo 664    = wceq 1289    e. wcel 1438   +oocpnf 7498   NN0cn0 8643  NN0*cxnn0 8706
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-13 1449  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-pow 4001  ax-un 4251  ax-cnex 7415
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3001  df-in 3003  df-ss 3010  df-pw 3427  df-sn 3447  df-pr 3448  df-uni 3649  df-pnf 7503  df-xr 7505  df-xnn0 8707
This theorem is referenced by:  inftonninf  9812
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