ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  c0ex GIF version

Theorem c0ex 7426
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
StepHypRef Expression
1 0cn 7424 . 2 0 ∈ ℂ
21elexi 2625 1 0 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1436  Vcvv 2615  cc 7292  0cc0 7294
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 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-ext 2067  ax-1cn 7382  ax-icn 7384  ax-addcl 7385  ax-mulcl 7387  ax-i2m1 7394
This theorem depends on definitions:  df-bi 115  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-v 2617
This theorem is referenced by:  elnn0  8608  nn0ex  8612  un0mulcl  8640  nn0ssz  8701  nn0ind-raph  8796  iser0f  9848  fser0const  9849  facnn  10031  fac0  10032  prhash2ex  10113  iserige0  10623  sum0  10666  isumz  10667  fisumss  10670  bezoutlemmain  10862  lcmval  10920
  Copyright terms: Public domain W3C validator