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Theorem riotasv2d 6586
 Description: Value of description binder for a single-valued class expression (as in e.g. reusv2 4721). Special case of riota2f 6563. (Contributed by NM, 2-Mar-2013.)
Hypotheses
Ref Expression
riotasv2d.1
riotasv2d.2
riotasv2d.3
riotasv2d.4
riotasv2d.5
riotasv2d.6
riotasv2d.7
riotasv2d.8
riotasv2d.9
Assertion
Ref Expression
riotasv2d
Distinct variable groups:   ,,   ,,   ,   ,   ,
Allowed substitution hints:   (,)   ()   (,)   ()   (,)   ()   (,)   (,)

Proof of Theorem riotasv2d
StepHypRef Expression
1 elex 2956 . 2
2 riotasv2d.8 . . . 4
4 riotasv2d.9 . . . 4
6 eleq1 2495 . . . . . . . 8
76adantl 453 . . . . . . 7
8 riotasv2d.5 . . . . . . 7
97, 8anbi12d 692 . . . . . 6
10 riotasv2d.6 . . . . . . 7
1110eqeq2d 2446 . . . . . 6
129, 11imbi12d 312 . . . . 5
1312adantlr 696 . . . 4
14 riotasv2d.4 . . . . 5
15 riotasv2d.7 . . . . 5
1614, 15riotasvd 6584 . . . 4
17 riotasv2d.1 . . . . 5
18 nfv 1629 . . . . 5
1917, 18nfan 1846 . . . 4
20 nfcvd 2572 . . . 4
21 nfvd 1630 . . . . . . 7
22 riotasv2d.3 . . . . . . 7
2321, 22nfand 1843 . . . . . 6
24 nfra1 2748 . . . . . . . . 9
25 nfcv 2571 . . . . . . . . 9
2624, 25nfriota 6551 . . . . . . . 8
2717, 14nfceqdf 2570 . . . . . . . 8
2826, 27mpbiri 225 . . . . . . 7
29 riotasv2d.2 . . . . . . 7
3028, 29nfeqd 2585 . . . . . 6
3123, 30nfimd 1827 . . . . 5
3231adantr 452 . . . 4
333, 13, 16, 19, 20, 32vtocldf 2995 . . 3
343, 5, 33mp2and 661 . 2
351, 34sylan2 461 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652   wcel 1725  wnfc 2558  wral 2697  cvv 2948  crio 6534 This theorem is referenced by:  riotasv2s  6588  cdleme42b  31176 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-nel 2601  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-undef 6535  df-riota 6541
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