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Theorem riotabidv 5391
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 445 . . 3
43iotabidv 4811 . 2  iota 
iota
5 df-riota 5389 . 2  iota_  iota
6 df-riota 5389 . 2  iota_  iota
74, 5, 63eqtr4g 2075 1  iota_  iota_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1226   wcel 1370   iotacio 4788   iota_crio 5388
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 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-rex 2286  df-uni 3551  df-iota 4790  df-riota 5389
This theorem is referenced by:  riotaeqbidv  5392  csbriotag  5400  subval  6805
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