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Theorem iunrab 4130
 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 4129 . 2
2 df-rab 2706 . . . 4
32a1i 11 . . 3
43iuneq2i 4103 . 2
5 df-rab 2706 . . 3
6 r19.42v 2854 . . . 4
76abbii 2547 . . 3
85, 7eqtr4i 2458 . 2
91, 4, 83eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  cab 2421  wrex 2698  crab 2701  ciun 4085 This theorem is referenced by:  incexc2  12610  itg2monolem1  19634  aannenlem1  20237  musum  20968  lgsquadlem1  21130  lgsquadlem2  21131  cnambfre  26245  fiphp3d  26871  phisum  27486  mapdval3N  32366  mapdval5N  32368 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-in 3319  df-ss 3326  df-iun 4087
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