Theorem iunxdif2 4378

Description: Indexed union with a class difference as its index. (Contributed by NM, 10-Dec-2004.)

Hypothesis

Ref	Expression
iunxdif2.1

Assertion

Ref	Expression
iunxdif2

Distinct variable groups:   ,,   ,,   ,   ,

Proof of Theorem iunxdif2

Step	Hyp	Ref	Expression
1		iunss2 4375	. . 3
2		difss 3630	. . . . 5
3		iunss1 4342	. . . . 5
4	2, 3	ax-mp 5	. . . 4
5		iunxdif2.1	. . . . 5
6	5	cbviunv 4369	. . . 4
7	4, 6	sseqtr4i 3536	. . 3
8	1, 7	jctil 537	. 2
9		eqss 3518	. 2
10	8, 9	sylibr 212	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  A.wral 2807  E.wrex 2808  \cdif 3472  C_wss 3475  U_ciun 4330

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-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-iun 4332