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Theorem disjeq2 4431
 Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjeq2 Disj Disj

Proof of Theorem disjeq2
StepHypRef Expression
1 eqimss2 3552 . . . 4
21ralimi 2850 . . 3
3 disjss2 4430 . . 3 Disj Disj
42, 3syl 16 . 2 Disj Disj
5 eqimss 3551 . . . 4
65ralimi 2850 . . 3
7 disjss2 4430 . . 3 Disj Disj
86, 7syl 16 . 2 Disj Disj
94, 8impbid 191 1 Disj Disj
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1395  wral 2807   wss 3471  Disj wdisj 4427 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rmo 2815  df-in 3478  df-ss 3485  df-disj 4428 This theorem is referenced by:  disjeq2dv  4432  voliun  22090  carsgclctunlem2  28461  mblfinlem2  30236  voliunnfl  30242
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