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

Step	Hyp	Ref	Expression
1		iunab 4376	. 2
2		df-rab 2816	. . . 4
3	2	a1i 11	. . 3
4	3	iuneq2i 4349	. 2
5		df-rab 2816	. . 3
6		r19.42v 3012	. . . 4
7	6	abbii 2591	. . 3
8	5, 7	eqtr4i 2489	. 2
9	1, 4, 8	3eqtr4i 2496	1

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