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Theorem pnfex 10295
Description: Plus infinity exists. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
pnfex +∞ ∈ V

Proof of Theorem pnfex
StepHypRef Expression
1 pnfxr 10294 . 2 +∞ ∈ ℝ*
21elexi 3365 1 +∞ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2145  Vcvv 3351  +∞cpnf 10273  *cxr 10275
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-8 2147  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-pow 4974  ax-un 7096  ax-cnex 10194
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rex 3067  df-v 3353  df-un 3728  df-in 3730  df-ss 3737  df-pw 4299  df-sn 4317  df-pr 4319  df-uni 4575  df-pnf 10278  df-xr 10280
This theorem is referenced by:  mnfxr  10298  elxnn0  11568  elxr  12151  xnegex  12240  xaddval  12255  xmulval  12257  xrinfmss  12341  hashgval  13320  hashinf  13322  hashfxnn0  13324  hashfOLD  13326  pcval  15752  pc0  15762  ramcl2  15923  iccpnfhmeo  22960  taylfval  24329  xrlimcnp  24912  xrge0iifcv  30316  xrge0iifiso  30317  xrge0iifhom  30319  sge0f1o  41113  sge0sup  41122  sge0pnfmpt  41176
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