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Theorem zfun 6593
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 6592 . 2
2 elequ2 1823 . . . . . . 7
3 elequ1 1821 . . . . . . 7
42, 3anbi12d 710 . . . . . 6
54cbvexv 2024 . . . . 5
65imbi1i 325 . . . 4
76albii 1640 . . 3
87exbii 1667 . 2
91, 8mpbi 208 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
This theorem is referenced by:  uniex2  6595  axunndlem1  8991
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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