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Theorem bdcriota 9318
Description: A class given by a restricted definition binder is bounded, under the given hypotheses. (Contributed by BJ, 24-Nov-2019.)
Hypotheses
Ref Expression
bdcriota.bd BOUNDED
bdcriota.ex
Assertion
Ref Expression
bdcriota BOUNDED  iota_
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bdcriota
Dummy variables  t are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bdcriota.bd . . . . . . . . 9 BOUNDED
21ax-bdsb 9257 . . . . . . . 8 BOUNDED
3 ax-bdel 9256 . . . . . . . 8 BOUNDED  t
42, 3ax-bdim 9249 . . . . . . 7 BOUNDED  t
54ax-bdal 9253 . . . . . 6 BOUNDED  t
6 df-ral 2305 . . . . . . . . 9  t  t
7 impexp 250 . . . . . . . . . . 11  t  t
87bicomi 123 . . . . . . . . . 10  t  t
98albii 1356 . . . . . . . . 9  t  t
106, 9bitri 173 . . . . . . . 8  t  t
11 sban 1826 . . . . . . . . . . . 12
12 clelsb3 2139 . . . . . . . . . . . . 13
1312anbi1i 431 . . . . . . . . . . . 12
1411, 13bitri 173 . . . . . . . . . . 11
1514bicomi 123 . . . . . . . . . 10
1615imbi1i 227 . . . . . . . . 9  t  t
1716albii 1356 . . . . . . . 8  t  t
1810, 17bitri 173 . . . . . . 7  t  t
19 df-clab 2024 . . . . . . . . . 10  {  |  }
2019bicomi 123 . . . . . . . . 9  {  |  }
2120imbi1i 227 . . . . . . . 8  t  {  |  }  t
2221albii 1356 . . . . . . 7  t 
{  |  }  t
2318, 22bitri 173 . . . . . 6  t  {  |  }  t
245, 23bd0 9259 . . . . 5 BOUNDED  {  |  }  t
2524bdcab 9284 . . . 4 BOUNDED  { t  |  {  |  }  t  }
26 df-int 3607 . . . 4  |^| {  |  }  { t  |  {  |  }  t  }
2725, 26bdceqir 9279 . . 3 BOUNDED 
|^| {  |  }
28 bdcriota.ex . . . . 5
29 df-reu 2307 . . . . 5
3028, 29mpbi 133 . . . 4
31 iotaint 4823 . . . 4  iota  |^| {  |  }
3230, 31ax-mp 7 . . 3  iota 
|^| {  |  }
3327, 32bdceqir 9279 . 2 BOUNDED  iota
34 df-riota 5411 . 2  iota_  iota
3533, 34bdceqir 9279 1 BOUNDED  iota_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   wceq 1242   wcel 1390  wsb 1642  weu 1897   {cab 2023  wral 2300  wreu 2302   |^|cint 3606   iotacio 4808   iota_crio 5410  BOUNDED wbd 9247  BOUNDED wbdc 9275
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  ax-bd0 9248  ax-bdim 9249  ax-bdal 9253  ax-bdel 9256  ax-bdsb 9257
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-reu 2307  df-v 2553  df-sbc 2759  df-un 2916  df-in 2918  df-sn 3373  df-pr 3374  df-uni 3572  df-int 3607  df-iota 4810  df-riota 5411  df-bdc 9276
This theorem is referenced by: (None)
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