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Theorem iunrab 4378
 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 4377 . 2
2 df-rab 2826 . . . 4
32a1i 11 . . 3
43iuneq2i 4350 . 2
5 df-rab 2826 . . 3
6 r19.42v 3021 . . . 4
76abbii 2601 . . 3
85, 7eqtr4i 2499 . 2
91, 4, 83eqtr4i 2506 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1379   wcel 1767  cab 2452  wrex 2818  crab 2821  ciun 4331 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-in 3488  df-ss 3495  df-iun 4333 This theorem is referenced by:  incexc2  13630  itg2monolem1  22025  aannenlem1  22591  musum  23333  lgsquadlem1  23495  lgsquadlem2  23496  iunpreima  27255  cnambfre  29990  fiphp3d  30681  phisum  31088  mapdval3N  36829  mapdval5N  36831
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