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Theorem rabun2 3622
 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 2716 . 2
2 df-rab 2716 . . . 4
3 df-rab 2716 . . . 4
42, 3uneq12i 3501 . . 3
5 elun 3490 . . . . . . 7
65anbi1i 678 . . . . . 6
7 andir 840 . . . . . 6
86, 7bitri 242 . . . . 5
98abbii 2550 . . . 4
10 unab 3610 . . . 4
119, 10eqtr4i 2461 . . 3
124, 11eqtr4i 2461 . 2
131, 12eqtr4i 2461 1
 Colors of variables: wff set class Syntax hints:   wo 359   wa 360   wceq 1653   wcel 1726  cab 2424  crab 2711   cun 3320 This theorem is referenced by:  fnsuppres  5955 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-un 3327
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