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Theorem dfiunv2 3693
 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 3659 . . . 4
21a1i 9 . . 3
32iuneq2i 3675 . 2
4 df-iun 3659 . 2
5 vex 2560 . . . . 5
6 eleq1 2100 . . . . . 6
76rexbidv 2327 . . . . 5
85, 7elab 2687 . . . 4
98rexbii 2331 . . 3
109abbii 2153 . 2
113, 4, 103eqtri 2064 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cab 2026  wrex 2307  ciun 3657 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-iun 3659 This theorem is referenced by: (None)
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