Theorem uni1ex 4294

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 4293	. 2 ⊢ (A ∈ V → ⋃1A ∈ V)
3	1, 2	ax-mp 5	1 ⊢ ⋃1A ∈ V

Syntax hints:   ∈ wcel 1710  Vcvv 2860  ⋃₁cuni1 4134

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-typlower 4087  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-uni 3893  df-opk 4059  df-1c 4137  df-uni1 4139  df-xpk 4186  df-cnvk 4187  df-p6 4192

This theorem is referenced by:  ncfinraiselem2  4481  nnpweqlem1  4523  sfintfinlem1  4532  tfinnnlem1  4534  vfinspclt  4553  1stex  4740  ssetex  4745  enpw1lem1  6062  nenpw1pwlem1  6085  nmembers1lem1  6269  nchoicelem16  6305  nchoicelem18  6307