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Theorem riotaprop 5491
 Description: Properties of a restricted definite description operator. Todo (df-riota 5468 update): can some uses of riota2f 5489 be shortened with this? (Contributed by NM, 23-Nov-2013.)
Hypotheses
Ref Expression
riotaprop.0
riotaprop.1
riotaprop.2
Assertion
Ref Expression
riotaprop
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotaprop
StepHypRef Expression
1 riotaprop.1 . . 3
2 riotacl 5482 . . 3
31, 2syl5eqel 2124 . 2
41eqcomi 2044 . . . 4
5 nfriota1 5475 . . . . . 6
61, 5nfcxfr 2175 . . . . 5
7 riotaprop.0 . . . . 5
8 riotaprop.2 . . . . 5
96, 7, 8riota2f 5489 . . . 4
104, 9mpbiri 157 . . 3
113, 10mpancom 399 . 2
123, 11jca 290 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wnf 1349   wcel 1393  wreu 2308  crio 5467 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-reu 2313  df-rab 2315  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-uni 3581  df-iota 4867  df-riota 5468 This theorem is referenced by: (None)
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