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Theorem pnfex 8007
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 8006 . 2  |- +oo  e.  RR*
21elexi 2749 1  |- +oo  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 2148   _Vcvv 2737   +oocpnf 7985   RR*cxr 7987
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-sep 4120  ax-pow 4173  ax-un 4432  ax-cnex 7899
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-pw 3577  df-sn 3598  df-pr 3599  df-uni 3810  df-pnf 7990  df-xr 7992
This theorem is referenced by:  mnfxr  8010  elxnn0  9237  elxr  9772  fxnn0nninf  10433  pc0  12296
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