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Theorem pnfex 11213
Description: Plus infinity exists. (Contributed by David A. Wheeler, 8-Dec-2018.) (Revised by Steven Nguyen, 7-Dec-2022.)
Assertion
Ref Expression
pnfex +∞ ∈ V

Proof of Theorem pnfex
StepHypRef Expression
1 df-pnf 11196 . 2 +∞ = 𝒫
2 cnex 11137 . . . 4 ℂ ∈ V
32uniex 7679 . . 3 ℂ ∈ V
43pwex 5336 . 2 𝒫 ℂ ∈ V
51, 4eqeltri 2830 1 +∞ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3444  𝒫 cpw 4561   cuni 4866  cc 11054  +∞cpnf 11191
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5257  ax-pow 5321  ax-un 7673  ax-cnex 11112
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-in 3918  df-ss 3928  df-pw 4563  df-uni 4867  df-pnf 11196
This theorem is referenced by:  pnfxr  11214  mnfxr  11217  elxnn0  12492  elxr  13042  xnegex  13133  xaddval  13148  xmulval  13150  xrinfmss  13235  hashgval  14239  hashinf  14241  hashfxnn0  14243  pcval  16721  pc0  16731  ramcl2  16893  iccpnfhmeo  24324  taylfval  25734  xrlimcnp  26334  xrge0iifcv  32572  xrge0iifiso  32573  xrge0iifhom  32575  sge0f1o  44709  sge0sup  44718  sge0pnfmpt  44772
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