Theorem riotasbc 6273

Description: Substitution law for descriptions. Compare iotasbc 31326. (Contributed by NM, 23-Aug-2011.) (Proof shortened by Mario Carneiro, 24-Dec-2016.)

Assertion

Ref	Expression
riotasbc

Proof of Theorem riotasbc

Step	Hyp	Ref	Expression
1		rabssab 3586	. . 3
2		riotacl2 6271	. . 3
3	1, 2	sseldi 3501	. 2
4		df-sbc 3328	. 2
5	3, 4	sylibr 212	1

Syntax hints:  ->wi 4  e.wcel 1818  {cab 2442  E!wreu 2809  {crab 2811  [.wsbc 3327  iota_crio 6256

This theorem is referenced by:  riotass2  6284  riotass  6285  cjth  12936  joinlem  15641  meetlem  15655  riotasvd  34687  lshpkrlem3  34837

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-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257