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Theorem dfiunv2 26019
 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 3923 . . . 4
21a1i 10 . . 3
32iuneq2i 3939 . 2
4 df-iun 3923 . 2
5 vex 2804 . . . . 5
6 eleq1 2356 . . . . . 6
76rexbidv 2577 . . . . 5
85, 7elab 2927 . . . 4
98rexbii 2581 . . 3
109abbii 2408 . 2
113, 4, 103eqtri 2320 1
 Colors of variables: wff set class Syntax hints:   wceq 1632   wcel 1696  cab 2282  wrex 2557  ciun 3921 This theorem is referenced by:  prismorcsetlemc  26020 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179  df-iun 3923
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