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Theorem dfiunv2 4366
Description: Define double indexed union. (Contributed by FL, 6-Nov-2013.)
Assertion
Ref Expression
dfiunv2
Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem dfiunv2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 4332 . . . 4
21a1i 11 . . 3
32iuneq2i 4349 . 2
4 df-iun 4332 . 2
5 vex 3112 . . . . 5
6 eleq1 2529 . . . . . 6
76rexbidv 2968 . . . . 5
85, 7elab 3246 . . . 4
98rexbii 2959 . . 3
109abbii 2591 . 2
113, 4, 103eqtri 2490 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  E.wrex 2808  U_ciun 4330
This theorem is referenced by:  2wot2wont  24886  2spot2iun2spont  24891  usg2spot2nb  25065
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-iun 4332
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