Theorem cnvkex 4287

Description: The Kuratowski converse of a set is a set. (Contributed by SF, 14-Jan-2015.)

Hypothesis

Ref	Expression
cnvkex.1	|- A e. _V

Assertion

Ref	Expression
cnvkex	|- `'kA e. _V

Proof of Theorem cnvkex

Step	Hyp	Ref	Expression
1		cnvkex.1	. 2 |- A e. _V
2		cnvkexg 4286	. 2 |- (A e. _V -> `'kA e. _V)
3	1, 2	ax-mp 8	1 |- `'kA e. _V

Syntax hints:   e. wcel 1710  _Vcvv 2859  `'_kccnvk 4175

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-xp 4079  ax-cnv 4080  ax-sn 4087

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-opk 4058  df-xpk 4185  df-cnvk 4186

This theorem is referenced by:  idkex  4314  uniexg  4316  intexg  4319  nncaddccl  4419  nnsucelrlem1  4424  preaddccan2lem1  4454  ltfintrilem1  4465  ncfinlowerlem1  4482  tfinrelkex  4487  oddfinex  4504  evenodddisjlem1  4515  nnpweqlem1  4522  sfintfinlem1  4531  tfinnnlem1  4533  vfinspclt  4552  opexg  4587  proj1exg  4591  proj2exg  4592  phialllem1  4616  setconslem5  4735  1stex  4739  swapex  4742  ssetex  4744  coexg  4749  siexg  4752