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Theorem rabun2 3776
Description: Abstraction restricted to a union. (Contributed by Stefan O'Rear, 5-Feb-2015.)
Assertion
Ref Expression
rabun2

Proof of Theorem rabun2
StepHypRef Expression
1 df-rab 2816 . 2
2 df-rab 2816 . . . 4
3 df-rab 2816 . . . 4
42, 3uneq12i 3655 . . 3
5 elun 3644 . . . . . . 7
65anbi1i 695 . . . . . 6
7 andir 868 . . . . . 6
86, 7bitri 249 . . . . 5
98abbii 2591 . . . 4
10 unab 3764 . . . 4
119, 10eqtr4i 2489 . . 3
124, 11eqtr4i 2489 . 2
131, 12eqtr4i 2489 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  u.cun 3473
This theorem is referenced by:  fnsuppresOLD  6131  fnsuppres  6946  lfinun  20026
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-un 3480
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