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Theorem riotaprop 5542
 Description: Properties of a restricted definite description operator. Todo (df-riota 5519 update): can some uses of riota2f 5540 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 5533 . . 3
31, 2syl5eqel 2169 . 2
41eqcomi 2087 . . . 4
5 nfriota1 5526 . . . . . 6
61, 5nfcxfr 2220 . . . . 5
7 riotaprop.0 . . . . 5
8 riotaprop.2 . . . . 5
96, 7, 8riota2f 5540 . . . 4
104, 9mpbiri 166 . . 3
113, 10mpancom 413 . 2
123, 11jca 300 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285  wnf 1390   wcel 1434  wreu 2355  crio 5518 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-reu 2360  df-rab 2362  df-v 2612  df-sbc 2825  df-un 2986  df-in 2988  df-ss 2995  df-sn 3422  df-pr 3423  df-uni 3622  df-iota 4917  df-riota 5519 This theorem is referenced by:  lble  8144
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