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Theorem riotaeqdv 6553
 Description: Formula-building deduction rule for iota. (Contributed by NM, 15-Sep-2011.)
Hypothesis
Ref Expression
riotaeqdv.1
Assertion
Ref Expression
riotaeqdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotaeqdv
StepHypRef Expression
1 riotaeqdv.1 . . . . . . 7
21eleq2d 2505 . . . . . 6
32anbi1d 687 . . . . 5
43eubidv 2291 . . . 4
5 df-reu 2714 . . . 4
6 df-reu 2714 . . . 4
74, 5, 63bitr4g 281 . . 3
83iotabidv 5442 . . 3
92abbidv 2552 . . . 4
109fveq2d 5735 . . 3
117, 8, 10ifbieq12d 3763 . 2
12 df-riota 6552 . 2
13 df-riota 6552 . 2
1411, 12, 133eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  weu 2283  cab 2424  wreu 2709  cif 3741  cio 5419  cfv 5457  cund 6544  crio 6545 This theorem is referenced by:  riotaeqbidv  6555  grpinvpropd  14871  funtransport  25970  fvtransport  25971 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-riota 6552
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