Theorem iuneq12d 4356

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

Hypotheses

Ref	Expression
iuneq1d.1
iuneq12d.2

Assertion

Ref	Expression
iuneq12d

Distinct variable groups:   ,   ,   ,

Proof of Theorem iuneq12d

Step	Hyp	Ref	Expression
1		iuneq1d.1	. . 3
2	1	iuneq1d 4355	. 2
3		iuneq12d.2	. . . 4
4	3	adantr 465	. . 3
5	4	iuneq2dv 4352	. 2
6	2, 5	eqtrd 2498	1

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

This theorem is referenced by:  otiunsndisj  4758  cfsmolem  8671  cfsmo  8672  wunex2  9137  wuncval2  9146  imasval  14908  lpival  17893  cnextval  20561  cnextfval  20562  dvfval  22301  2spotiundisj  25062  mblfinlem2  30052  heiborlem10  30316

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