Theorem iuneq2dv 4352

Description: Equality deduction for indexed union. (Contributed by NM, 3-Aug-2004.)

Hypothesis

Ref	Expression
iuneq2dv.1

Assertion

Ref	Expression
iuneq2dv

Distinct variable group:   ,

Proof of Theorem iuneq2dv

Step	Hyp	Ref	Expression
1		iuneq2dv.1	. . 3
2	1	ralrimiva 2871	. 2
3		iuneq2 4347	. 2
4	2, 3	syl 16	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  U_ciun 4330

This theorem is referenced by:  iuneq12d  4356  iuneq2d  4357  fparlem3  6902  fparlem4  6903  oalim  7201  omlim  7202  oelim  7203  oelim2  7263  r1val3  8277  imasdsval  14912  acsfn  15056  tgidm  19482  cmpsub  19900  alexsublem  20544  bcth3  21770  ovoliunlem1  21913  voliunlem1  21960  uniiccdif  21987  uniioombllem2  21992  uniioombllem3a  21993  uniioombllem4  21995  itg2monolem1  22157  taylpfval  22760  ofpreima2  27508  eulerpartlemgu  28316  cvmscld  28718  msubvrs  28920  mblfinlem2  30052  ftc1anclem6  30095  heibor  30317

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-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-v 3111  df-in 3482  df-ss 3489  df-iun 4332