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Theorem riotaund 6578
 Description: Restricted iota equals the undefined value of its domain of discourse when not meaningful. (Contributed by NM, 16-Jan-2012.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
riotaund
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem riotaund
StepHypRef Expression
1 iffalse 3738 . 2
2 df-riota 6541 . 2
3 abid2 2552 . . . 4
43eqcomi 2439 . . 3
54fveq2i 5723 . 2
61, 2, 53eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1652   wcel 1725  cab 2421  wreu 2699  cif 3731  cio 5408  cfv 5446  cund 6533  crio 6534 This theorem is referenced by:  riotaprc  6579  riotassuni  6580  riotaclbg  6581  riotaundb  6583 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-riota 6541
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