Theorem iuneq2d 4357

Description: Equality deduction for indexed union. (Contributed by Drahflow, 22-Oct-2015.)

Hypothesis

Ref	Expression
iuneq2d.2

Assertion

Ref	Expression
iuneq2d

Distinct variable groups:   ,   ,

Proof of Theorem iuneq2d

Step	Hyp	Ref	Expression
1		iuneq2d.2	. . 3
2	1	adantr 465	. 2
3	2	iuneq2dv 4352	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  U_ciun 4330

This theorem is referenced by:  iununi  4415  oelim2  7263  ituniiun  8823  imasval  14908  mreacs  15055  cnextval  20561  taylfval  22754  iunpreima  27432  msubvrs  28920  dfrtrclrec2  29066  rtrclreclem.refl  29067  rtrclreclem.subset  29068  rtrclreclem.min  29070  trpredeq1  29303  trpredeq2  29304  voliunnfl  30058  neibastop2  30179  sstotbnd2  30270  equivtotbnd  30274  totbndbnd  30285  heiborlem3  30309  otiunsndisjX  32301

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