Theorem sikex 4298

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

Hypothesis

Ref	Expression
sikex.1	⊢ A ∈ V

Assertion

Ref	Expression
sikex	⊢ SIk A ∈ V

Proof of Theorem sikex

Step	Hyp	Ref	Expression
1		sikex.1	. 2 ⊢ A ∈ V
2		sikexg 4297	. 2 ⊢ (A ∈ V → SIk A ∈ V)
3	1, 2	ax-mp 5	1 ⊢ SIk A ∈ V

Syntax hints:   ∈ wcel 1710  Vcvv 2860   SI_k csik 4182

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 4079  ax-xp 4080  ax-cnv 4081  ax-1c 4082  ax-si 4084  ax-sn 4088

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 2479  df-ne 2519  df-ral 2620  df-rex 2621  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-un 3215  df-dif 3216  df-ss 3260  df-nul 3552  df-sn 3742  df-pr 3743  df-opk 4059  df-1c 4137  df-xpk 4186  df-cnvk 4187  df-sik 4193

This theorem is referenced by:  addcexlem  4383  nncex  4397  nnsucelrlem1  4425  ltfinex  4465  ncfinraiselem2  4481  ncfinlowerlem1  4483  tfinrelkex  4488  evenfinex  4504  oddfinex  4505  evenodddisjlem1  4516  nnadjoinlem1  4520  nnpweqlem1  4523  srelkex  4526  sfintfinlem1  4532  tfinnnlem1  4534  spfinex  4538  setconslem5  4736  1stex  4740  swapex  4743