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Theorem riotaprop 6290
 Description: Properties of a restricted definite description operator. Todo (df-riota 6267 update): can some uses of riota2f 6288 be shortened with this? (Contributed by NM, 23-Nov-2013.)
Hypotheses
Ref Expression
riotaprop.0
riotaprop.1
riotaprop.2
Assertion
Ref Expression
riotaprop
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotaprop
StepHypRef Expression
1 riotaprop.1 . . 3
2 riotacl 6281 . . 3
31, 2syl5eqel 2511 . 2
41eqcomi 2435 . . . 4
5 nfriota1 6274 . . . . . 6
61, 5nfcxfr 2578 . . . . 5
7 riotaprop.0 . . . . 5
8 riotaprop.2 . . . . 5
96, 7, 8riota2f 6288 . . . 4
104, 9mpbiri 236 . . 3
113, 10mpancom 673 . 2
123, 11jca 534 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wnf 1661   wcel 1872  wreu 2773  crio 6266 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2273  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-reu 2778  df-rab 2780  df-v 3082  df-sbc 3300  df-un 3441  df-in 3443  df-ss 3450  df-sn 3999  df-pr 4001  df-uni 4220  df-iota 5565  df-riota 6267 This theorem is referenced by:  fin23lem27  8765  lble  10565  ltrniotaval  34117
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