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Theorem disjeq2dv 4427
Description: Equality deduction for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypothesis
Ref Expression
disjeq2dv.1
Assertion
Ref Expression
disjeq2dv
Distinct variable group:   ,

Proof of Theorem disjeq2dv
StepHypRef Expression
1 disjeq2dv.1 . . 3
21ralrimiva 2871 . 2
3 disjeq2 4426 . 2
42, 3syl 16 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  Disj_wdisj 4422
This theorem is referenced by:  disjeq12d  4431  iunmbl  21963  uniioovol  21988  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
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