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Theorem iunrab 3704
 Description: The indexed union of a restricted class abstraction. (Contributed by NM, 3-Jan-2004.) (Proof shortened by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
iunrab
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem iunrab
StepHypRef Expression
1 iunab 3703 . 2
2 df-rab 2315 . . . 4
32a1i 9 . . 3
43iuneq2i 3675 . 2
5 df-rab 2315 . . 3
6 r19.42v 2467 . . . 4
76abbii 2153 . . 3
85, 7eqtr4i 2063 . 2
91, 4, 83eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243   wcel 1393  cab 2026  wrex 2307  crab 2310  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-rab 2315  df-v 2559  df-in 2924  df-ss 2931  df-iun 3659 This theorem is referenced by: (None)
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