NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  uni1exg Unicode version

Theorem uni1exg 4293
Description: The unit union operator preserves sethood. (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
uni1exg 1

Proof of Theorem uni1exg
StepHypRef Expression
1 dfuni12 4292 . 2 1 P6 k
2 vvex 4110 . . . 4
3 xpkexg 4289 . . . 4 k
42, 3mpan 651 . . 3 k
5 p6exg 4291 . . 3 k P6 k
64, 5syl 15 . 2 P6 k
71, 6syl5eqel 2437 1 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wcel 1710  cvv 2860  ⋃1cuni1 4134   k cxpk 4175   P6 cp6 4179
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:  uni1ex  4294  uniexg  4317  intexg  4320  coexg  4750  siexg  4753
  Copyright terms: Public domain W3C validator