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

Step	Hyp	Ref	Expression
1		iota4 5574	. 2
2		df-sbc 3328	. 2
3	1, 2	sylib 196	1

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