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Theorem uniiun 3701
 Description: Class union in terms of indexed union. Definition in [Stoll] p. 43. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
uniiun A = x A x
Distinct variable group:   x,A

Proof of Theorem uniiun
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 dfuni2 3573 . 2 A = {yx A y x}
2 df-iun 3650 . 2 x A x = {yx A y x}
31, 2eqtr4i 2060 1 A = x A x
 Colors of variables: wff set class Syntax hints:   = wceq 1242  {cab 2023  ∃wrex 2301  ∪ cuni 3571  ∪ ciun 3648 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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-rex 2306  df-uni 3572  df-iun 3650 This theorem is referenced by:  iunpwss  3734  truni  3859  iunpw  4177  reluni  4403  rnuni  4678  imauni  5343
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