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Theorem riotaund 5445
Description: Restricted iota equals the empty set when not meaningful. (Contributed by NM, 16-Jan-2012.) (Revised by Mario Carneiro, 15-Oct-2016.) (Revised by NM, 13-Sep-2018.)
Assertion
Ref Expression
riotaund  iota_  (/)
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem riotaund
StepHypRef Expression
1 df-riota 5411 . 2  iota_  iota
2 df-reu 2307 . . 3
3 iotanul 4825 . . 3  iota  (/)
42, 3sylnbi 602 . 2  iota  (/)
51, 4syl5eq 2081 1  iota_  (/)
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wceq 1242   wcel 1390  weu 1897  wreu 2302   (/)c0 3218   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-in1 544  ax-in2 545  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-bndl 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-fal 1248  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-dif 2914  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-uni 3572  df-iota 4810  df-riota 5411
This theorem is referenced by: (None)
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