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Theorem riotabidv 5413
Description: Formula-building deduction rule for restricted iota. (Contributed by NM, 15-Sep-2011.)
Hypothesis
Ref Expression
riotabidv.1
Assertion
Ref Expression
riotabidv  iota_  iota_
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotabidv
StepHypRef Expression
1 biidd 161 . . . 4
2 riotabidv.1 . . . 4
31, 2anbi12d 442 . . 3
43iotabidv 4831 . 2  iota 
iota
5 df-riota 5411 . 2  iota_  iota
6 df-riota 5411 . 2  iota_  iota
74, 5, 63eqtr4g 2094 1  iota_  iota_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   wcel 1390   iotacio 4808   iota_crio 5410
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-uni 3572  df-iota 4810  df-riota 5411
This theorem is referenced by:  riotaeqbidv  5414  csbriotag  5423  subval  6980  divvalap  7415  divfnzn  8312  cjval  9053  sqrtrval  9189
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