Theorem uni1ex 4293

Description: The unit union operator preserves sethood. (Contributed by SF, 14-Jan-2015.)

Hypothesis

Ref	Expression
uni1ex.1	⊢ A ∈ V

Assertion

Ref	Expression
uni1ex	⊢ ⋃1A ∈ V

Proof of Theorem uni1ex

Step	Hyp	Ref	Expression
1		uni1ex.1	. 2 ⊢ A ∈ V
2		uni1exg 4292	. 2 ⊢ (A ∈ V → ⋃1A ∈ V)
3	1, 2	ax-mp 5	1 ⊢ ⋃1A ∈ V

Syntax hints:   ∈ wcel 1710  Vcvv 2859  ⋃₁cuni1 4133

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 4078  ax-xp 4079  ax-cnv 4080  ax-typlower 4086  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-uni 3892  df-opk 4058  df-1c 4136  df-uni1 4138  df-xpk 4185  df-cnvk 4186  df-p6 4191

This theorem is referenced by:  ncfinraiselem2  4480  nnpweqlem1  4522  sfintfinlem1  4531  tfinnnlem1  4533  vfinspclt  4552  1stex  4739  ssetex  4744  enpw1lem1  6061  nenpw1pwlem1  6084  nmembers1lem1  6268  nchoicelem16  6304  nchoicelem18  6306