Theorem iuneq2 4347

Description: Equality theorem for indexed union. (Contributed by NM, 22-Oct-2003.)

Assertion

Ref	Expression
iuneq2

Proof of Theorem iuneq2

Step	Hyp	Ref	Expression
1		ss2iun 4346	. . 3
2		ss2iun 4346	. . 3
3	1, 2	anim12i 566	. 2
4		eqss 3518	. . . 4
5	4	ralbii 2888	. . 3
6		r19.26 2984	. . 3
7	5, 6	bitri 249	. 2
8		eqss 3518	. 2
9	3, 7, 8	3imtr4i 266	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  A.wral 2807  C_wss 3475  U_ciun 4330

This theorem is referenced by:  iuneq2i  4349  iuneq2dv  4352  oa0r  7207  om0r  7208  om1r  7211  oe1m  7213  oaass  7229  oarec  7230  omass  7248  oeoalem  7264  oeoelem  7266  cardiun  8384  kmlem11  8561  iuncld  19546  comppfsc  20033  istotbnd3  30267  sstotbnd  30271  heibor  30317  iuneq12f  30572

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