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Theorem riotasbc 6280
 Description: Substitution law for descriptions. Compare iotasbc 36672. (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 3549 . . 3
2 riotacl2 6278 . . 3
31, 2sseldi 3463 . 2
4 df-sbc 3301 . 2
53, 4sylibr 216 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1869  cab 2408  wreu 2778  crab 2780  wsbc 3300  crio 6264 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-rex 2782  df-reu 2783  df-rab 2785  df-v 3084  df-sbc 3301  df-un 3442  df-in 3444  df-ss 3451  df-sn 3998  df-pr 4000  df-uni 4218  df-iota 5563  df-riota 6265 This theorem is referenced by:  riotass2  6291  riotass  6292  cjth  13160  joinlem  16250  meetlem  16264  finxpreclem4  31744  poimirlem26  31924  riotasvd  32491  lshpkrlem3  32641
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