MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3ex Structured version   Visualization version   GIF version

Theorem 3ex 12229
Description: The number 3 is a set. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
3ex 3 ∈ V

Proof of Theorem 3ex
StepHypRef Expression
1 3cn 12228 . 2 3 ∈ ℂ
21elexi 3461 1 3 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2109  Vcvv 3438  cc 11026  3c3 12203
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-1cn 11086  ax-addcl 11088
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3440  df-2 12210  df-3 12211
This theorem is referenced by:  fztpval  13508  funcnvs4  14841  iblcnlem1  25706  basellem9  27016  lgsdir2lem3  27255  axlowdimlem7  28912  axlowdimlem8  28913  axlowdimlem9  28914  axlowdimlem13  28918  3wlkdlem4  30125  3pthdlem1  30127  upgr4cycl4dv4e  30148  konigsberglem4  30218  konigsberglem5  30219  ex-pss  30391  ex-fv  30406  ex-1st  30407  ex-2nd  30408  rabren3dioph  42808  lhe4.4ex1a  44322  nnsum4primesodd  47800  nnsum4primesoddALTV  47801  usgrexmpl1lem  48025  usgrexmpl2lem  48030  usgrexmpl2nb0  48035  usgrexmpl2nb1  48036  usgrexmpl2nb2  48037  usgrexmpl2nb3  48038  usgrexmpl2nb4  48039  usgrexmpl2trifr  48041  zlmodzxzldeplem  48503
  Copyright terms: Public domain W3C validator