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Theorem dfiunv2 4305
 Description: Define double indexed union. (Contributed by FL, 6-Nov-2013.)
Assertion
Ref Expression
dfiunv2
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem dfiunv2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 4271 . . . 4
21a1i 11 . . 3
32iuneq2i 4288 . 2
4 df-iun 4271 . 2
5 vex 3034 . . . . 5
6 eleq1 2537 . . . . . 6
76rexbidv 2892 . . . . 5
85, 7elab 3173 . . . 4
98rexbii 2881 . . 3
109abbii 2587 . 2
113, 4, 103eqtri 2497 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   wcel 1904  cab 2457  wrex 2757  ciun 4269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-in 3397  df-ss 3404  df-iun 4271 This theorem is referenced by:  2wot2wont  25693  2spot2iun2spont  25698  usg2spot2nb  25872
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