ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pnfex Unicode version

Theorem pnfex 8691
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 8690 . 2  |- +oo  e.  RR*
21elexi 2567 1  |- +oo  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1393   _Vcvv 2557   +oocpnf 7055   RR*cxr 7057
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-un 4170  ax-cnex 6973
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-uni 3581  df-pnf 7060  df-xr 7062
This theorem is referenced by:  mnfxr  8692  elxr  8694
  Copyright terms: Public domain W3C validator