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Theorem riotauni 6592
 Description: Restricted iota in terms of class union. (Contributed by NM, 11-Oct-2011.)
Assertion
Ref Expression
riotauni

Proof of Theorem riotauni
StepHypRef Expression
1 riotaiota 6591 . 2
2 df-reu 2719 . . . 4
3 iotauni 5465 . . . 4
42, 3sylbi 189 . . 3
5 df-rab 2721 . . . 4
65unieqi 4054 . . 3
74, 6syl6eqr 2493 . 2
81, 7eqtrd 2475 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1654   wcel 1728  weu 2288  cab 2429  wreu 2714  crab 2716  cuni 4044  cio 5451  crio 6578 This theorem is referenced by:  riotassuni  6624  supval2  7496  dfac2a  8048 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rex 2718  df-reu 2719  df-rab 2721  df-v 2967  df-sbc 3171  df-un 3314  df-if 3768  df-sn 3849  df-pr 3850  df-uni 4045  df-iota 5453  df-riota 6585
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