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Theorem riotaprop 6573
 Description: Properties of a restricted definite description operator. Todo: can some uses of riota2f 6571 be shortened with this? (Contributed by NM, 23-Nov-2013.)
Hypotheses
Ref Expression
riotaprop.0
riotaprop.1
riotaprop.3
Assertion
Ref Expression
riotaprop
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotaprop
StepHypRef Expression
1 riotaprop.1 . . 3
2 riotacl 6564 . . 3
31, 2syl5eqel 2520 . 2
41eqcomi 2440 . . . 4
5 nfriota1 6557 . . . . . 6
61, 5nfcxfr 2569 . . . . 5
7 riotaprop.0 . . . . 5
8 riotaprop.3 . . . . 5
96, 7, 8riota2f 6571 . . . 4
104, 9mpbiri 225 . . 3
113, 10mpancom 651 . 2
123, 11jca 519 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652   wcel 1725  wreu 2707  crio 6542 This theorem is referenced by:  fin23lem27  8208  lble  9960  ltrniotaval  31378 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 2417 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-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-riota 6549
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