MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  disjeq2 Unicode version

Theorem disjeq2 4426
Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjeq2

Proof of Theorem disjeq2
StepHypRef Expression
1 eqimss2 3556 . . . 4
21ralimi 2850 . . 3
3 disjss2 4425 . . 3
42, 3syl 16 . 2
5 eqimss 3555 . . . 4
65ralimi 2850 . . 3
7 disjss2 4425 . . 3
86, 7syl 16 . 2
94, 8impbid 191 1
Colors of variables: wff setvar class
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
  Copyright terms: Public domain W3C validator