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Theorem zfun 4356
 Description: Axiom of Union expressed with the fewest number of different variables. (Contributed by NM, 14-Aug-2003.)
Assertion
Ref Expression
zfun
Distinct variable group:   ,,

Proof of Theorem zfun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-un 4355 . 2
2 elequ2 1691 . . . . . . 7
3 elequ1 1690 . . . . . . 7
42, 3anbi12d 464 . . . . . 6
54cbvexv 1890 . . . . 5
65imbi1i 237 . . . 4
76albii 1446 . . 3
87exbii 1584 . 2
91, 8mpbi 144 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1329  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-13 1491  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-un 4355 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  uniex2  4358  bj-uniex2  13144
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