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Theorem pnfex 7520
Description: Plus infinity exists (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
pnfex  |- +oo  e.  _V

Proof of Theorem pnfex
StepHypRef Expression
1 pnfxr 7519 . 2  |- +oo  e.  RR*
21elexi 2631 1  |- +oo  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   _Vcvv 2619   +oocpnf 7498   RR*cxr 7500
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
This theorem is referenced by:  mnfxr  7523  elxnn0  8708  elxr  9216  fxnn0nninf  9809
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