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Theorem iotaeq 5565
 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 2091 . . . . . . 7
2 df-clab 2453 . . . . . . 7
3 df-clab 2453 . . . . . . 7
41, 2, 33bitr4g 288 . . . . . 6
54eqrdv 2464 . . . . 5
65eqeq1d 2469 . . . 4
76abbidv 2603 . . 3
87unieqd 4261 . 2
9 df-iota 5557 . 2
10 df-iota 5557 . 2
118, 9, 103eqtr4g 2533 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1377   wceq 1379  wsb 1711   wcel 1767  cab 2452  csn 4033  cuni 4251  cio 5555 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2823  df-uni 4252  df-iota 5557 This theorem is referenced by: (None)
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