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

Theorem 3ex 11707
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 11706 . 2 3 ∈ ℂ
21elexi 3511 1 3 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  Vcvv 3492  cc 10523  3c3 11681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790  ax-1cn 10583  ax-addcl 10585
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-v 3494  df-2 11688  df-3 11689
This theorem is referenced by:  fztpval  12957  funcnvs4  14265  iblcnlem1  24315  basellem9  25593  lgsdir2lem3  25830  axlowdimlem7  26661  axlowdimlem8  26662  axlowdimlem9  26663  axlowdimlem13  26667  3wlkdlem4  27868  3pthdlem1  27870  upgr4cycl4dv4e  27891  konigsberglem4  27961  konigsberglem5  27962  ex-pss  28134  ex-fv  28149  ex-1st  28150  ex-2nd  28151  rabren3dioph  39290  lhe4.4ex1a  40538  nnsum4primesodd  43838  nnsum4primesoddALTV  43839  zlmodzxzldeplem  44481
  Copyright terms: Public domain W3C validator