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Theorem iotaeq 4875
 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 1680 . . . . . . 7
2 df-clab 2027 . . . . . . 7
3 df-clab 2027 . . . . . . 7
41, 2, 33bitr4g 212 . . . . . 6
54eqrdv 2038 . . . . 5
65eqeq1d 2048 . . . 4
76abbidv 2155 . . 3
87unieqd 3591 . 2
9 df-iota 4867 . 2
10 df-iota 4867 . 2
118, 9, 103eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241   wceq 1243   wcel 1393  wsb 1645  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: (None)
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