Theorem c0ex 7113

Description: 0 is a set (common case). (Contributed by David A. Wheeler, 7-Jul-2016.)

Assertion

Ref	Expression
c0ex	⊢ 0 ∈ V

Proof of Theorem c0ex

Step	Hyp	Ref	Expression
1		0cn 7111	. 2 ⊢ 0 ∈ ℂ
2	1	elexi 2611	1 ⊢ 0 ∈ V

Syntax hints:   ∈ wcel 1433  Vcvv 2601  ℂcc 6979  0cc0 6981

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063  ax-1cn 7069  ax-icn 7071  ax-addcl 7072  ax-mulcl 7074  ax-i2m1 7081

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by:  elnn0  8290  nn0ex  8294  un0mulcl  8322  nn0ssz  8369  nn0ind-raph  8464  iser0f  9472  facnn  9654  fac0  9655  iserige0  10181  bezoutlemmain  10387  lcmval  10445