Theorem disjeq2 4426

Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)

Assertion

Ref	Expression
disjeq2

Proof of Theorem disjeq2

Step	Hyp	Ref	Expression
1		eqimss2 3556	. . . 4
2	1	ralimi 2850	. . 3
3		disjss2 4425	. . 3
4	2, 3	syl 16	. 2
5		eqimss 3555	. . . 4
6	5	ralimi 2850	. . 3
7		disjss2 4425	. . 3
8	6, 7	syl 16	. 2
9	4, 8	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  A.wral 2807  C_wss 3475  Disj_wdisj 4422

This theorem is referenced by:  disjeq2dv  4427  voliun  21964  mblfinlem2  30052  voliunnfl  30058

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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rmo 2815  df-in 3482  df-ss 3489  df-disj 4423