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Theorem iunrab 4377
 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:   ,   ,   ,

Proof of Theorem iunrab
StepHypRef Expression
1 iunab 4376 . 2
2 df-rab 2816 . . . 4
32a1i 11 . . 3
43iuneq2i 4349 . 2
5 df-rab 2816 . . 3
6 r19.42v 3012 . . . 4
76abbii 2591 . . 3
85, 7eqtr4i 2489 . 2
91, 4, 83eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  E.wrex 2808  {crab 2811  U_ciun 4330 This theorem is referenced by:  incexc2  13650  itg2monolem1  22157  aannenlem1  22724  musum  23467  lgsquadlem1  23629  lgsquadlem2  23630  iunpreima  27432  cnambfre  30063  fiphp3d  30753  phisum  31159  mapdval3N  37358  mapdval5N  37360 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-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489  df-iun 4332
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