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Theorem iunrab 4013
 Description: The indexed union of a restricted class abstraction. (Contributed by NM, 3-Jan-2004.) (Proof shortened by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
iunrab
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem iunrab
StepHypRef Expression
1 iunab 4012 . 2
2 df-rab 2623 . . . 4
32a1i 10 . . 3
43iuneq2i 3987 . 2
5 df-rab 2623 . . 3
6 r19.42v 2765 . . . 4
76abbii 2465 . . 3
85, 7eqtr4i 2376 . 2
91, 4, 83eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wa 358   wceq 1642   wcel 1710  cab 2339  wrex 2615  crab 2618  ciun 3969 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-ral 2619  df-rex 2620  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-iun 3971 This theorem is referenced by: (None)
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