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Theorem iotabi 4876
 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 2151 . . . . . 6
21biimpi 113 . . . . 5
32eqeq1d 2048 . . . 4
43abbidv 2155 . . 3
54unieqd 3591 . 2
6 df-iota 4867 . 2
7 df-iota 4867 . 2
85, 6, 73eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  cab 2026  csn 3375  cuni 3580  cio 4865 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-uni 3581  df-iota 4867 This theorem is referenced by:  iotabidv  4888  iotabii  4889  eusvobj1  5499
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