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Theorem iuneq1 3711
 Description: Equality theorem for indexed union. (Contributed by NM, 27-Jun-1998.)
Assertion
Ref Expression
iuneq1
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iuneq1
StepHypRef Expression
1 iunss1 3709 . . 3
2 iunss1 3709 . . 3
31, 2anim12i 331 . 2
4 eqss 3023 . 2
5 eqss 3023 . 2
63, 4, 53imtr4i 199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wceq 1285   wss 2982  ciun 3698 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-in 2988  df-ss 2995  df-iun 3700 This theorem is referenced by:  iuneq1d  3721  iununir  3779  iunsuc  4203  rdgisuc1  6053  rdg0  6056  oasuc  6128  omsuc  6136
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