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Theorem riotasbc 5483
 Description: Substitution law for descriptions. (Contributed by NM, 23-Aug-2011.) (Proof shortened by Mario Carneiro, 24-Dec-2016.)
Assertion
Ref Expression
riotasbc

Proof of Theorem riotasbc
StepHypRef Expression
1 rabssab 3027 . . 3
2 riotacl2 5481 . . 3
31, 2sseldi 2943 . 2
4 df-sbc 2765 . 2
53, 4sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1393  cab 2026  wreu 2308  crab 2310  wsbc 2764  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-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:  riotass2  5494  riotass  5495  cjth  9446
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