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Theorem iotaeq 5426
 Description: Equality theorem for descriptions. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
iotaeq

Proof of Theorem iotaeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 drsb1 2112 . . . . . . 7
2 df-clab 2423 . . . . . . 7
3 df-clab 2423 . . . . . . 7
41, 2, 33bitr4g 280 . . . . . 6
54eqrdv 2434 . . . . 5
65eqeq1d 2444 . . . 4
76abbidv 2550 . . 3
87unieqd 4026 . 2
9 df-iota 5418 . 2
10 df-iota 5418 . 2
118, 9, 103eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549   wceq 1652  wsb 1658   wcel 1725  cab 2422  csn 3814  cuni 4015  cio 5416 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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