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Theorem riota2f 5489
 Description: This theorem shows a condition that allows us to represent a descriptor with a class expression . (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
riota2f.1
riota2f.2
riota2f.3
Assertion
Ref Expression
riota2f
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riota2f
StepHypRef Expression
1 riota2f.1 . . 3
21nfel1 2188 . 2
31a1i 9 . 2
4 riota2f.2 . . 3
54a1i 9 . 2
6 id 19 . 2
7 riota2f.3 . . 3
87adantl 262 . 2
92, 3, 5, 6, 8riota2df 5488 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wnf 1349   wcel 1393  wnfc 2165  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-v 2559  df-sbc 2765  df-un 2922  df-sn 3381  df-pr 3382  df-uni 3581  df-iota 4867  df-riota 5468 This theorem is referenced by:  riota2  5490  riotaprop  5491  riotass2  5494  riotass  5495
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