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Theorem iotauni 5565
 Description: Equivalence between two different forms of . (Contributed by Andrew Salmon, 12-Jul-2011.)
Assertion
Ref Expression
iotauni

Proof of Theorem iotauni
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2323 . 2
2 iotaval 5564 . . . 4
3 uniabio 5563 . . . 4
42, 3eqtr4d 2508 . . 3
54exlimiv 1784 . 2
61, 5sylbi 200 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450   wceq 1452  wex 1671  weu 2319  cab 2457  cuni 4190  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-v 3033  df-sbc 3256  df-un 3395  df-sn 3960  df-pr 3962  df-uni 4191  df-iota 5553 This theorem is referenced by:  iotaint  5566  iotassuni  5569  dfiota4  5581  fveu  5871  riotauni  6276
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