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Theorem iotabi 5427
 Description: Equivalence theorem for descriptions. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
iotabi

Proof of Theorem iotabi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 abbi 2546 . . . . . 6
21biimpi 187 . . . . 5
32eqeq1d 2444 . . . 4
43abbidv 2550 . . 3
54unieqd 4026 . 2
6 df-iota 5418 . 2
7 df-iota 5418 . 2
85, 6, 73eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652  cab 2422  csn 3814  cuni 4015  cio 5416 This theorem is referenced by:  iotabidv  5439  iotabii  5440  eusvobj1  6583  iotasbcq  27614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-uni 4016  df-iota 5418
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