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Theorem rabun2 3534
 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 2623 . 2
2 df-rab 2623 . . . 4
3 df-rab 2623 . . . 4
42, 3uneq12i 3416 . . 3
5 elun 3220 . . . . . . 7
65anbi1i 676 . . . . . 6
7 andir 838 . . . . . 6
86, 7bitri 240 . . . . 5
98abbii 2465 . . . 4
10 unab 3521 . . . 4
119, 10eqtr4i 2376 . . 3
124, 11eqtr4i 2376 . 2
131, 12eqtr4i 2376 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wa 358   wceq 1642   wcel 1710  cab 2339  crab 2618   cun 3207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214 This theorem is referenced by: (None)
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