Theorem pnfex 11267

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

Step	Hyp	Ref	Expression
1		df-pnf 11250	. 2 ⊢ +∞ = 𝒫 ∪ ℂ
2		cnex 11191	. . . 4 ⊢ ℂ ∈ V
3	2	uniex 7731	. . 3 ⊢ ∪ ℂ ∈ V
4	3	pwex 5379	. 2 ⊢ 𝒫 ∪ ℂ ∈ V
5	1, 4	eqeltri 2830	1 ⊢ +∞ ∈ V

Syntax hints:   ∈ wcel 2107  Vcvv 3475  𝒫 cpw 4603  ∪ cuni 4909  ℂcc 11108  +∞cpnf 11245

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 5300  ax-pow 5364  ax-un 7725  ax-cnex 11166

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 3477  df-in 3956  df-ss 3966  df-pw 4605  df-uni 4910  df-pnf 11250

This theorem is referenced by:  pnfxr  11268  mnfxr  11271  elxnn0  12546  elxr  13096  xnegex  13187  xaddval  13202  xmulval  13204  xrinfmss  13289  hashgval  14293  hashinf  14295  hashfxnn0  14297  pcval  16777  pc0  16787  ramcl2  16949  iccpnfhmeo  24461  taylfval  25871  xrlimcnp  26473  xrge0iifcv  32914  xrge0iifiso  32915  xrge0iifhom  32917  sge0f1o  45098  sge0sup  45107  sge0pnfmpt  45161