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Theorem iotacl 5579
 Description: Membership law for descriptions. This can useful for expanding an unbounded iota-based definition (see df-iota 5556). If you have a bounded iota-based definition, riotacl2 6271 may be useful. (Contributed by Andrew Salmon, 1-Aug-2011.)
Assertion
Ref Expression
iotacl

Proof of Theorem iotacl
StepHypRef Expression
1 iota4 5574 . 2
2 df-sbc 3328 . 2
31, 2sylib 196 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818  E!weu 2282  {cab 2442  [.wsbc 3327  iotacio 5554 This theorem is referenced by:  riotacl2  6271  opiota  6859  eroprf  7428  iunfictbso  8516  isf32lem9  8762  psgnvali  16533  fourierdlem36  31925 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556
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