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Theorem riotasv3d 6598
 Description: A property holding for a representative of a single-valued class expression (see e.g. reusv2 4729) also holds for its description binder (in the form of property ). (Contributed by NM, 5-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
riotasv3d.1
riotasv3d.2
riotasv3d.3
riotasv3d.4
riotasv3d.5
riotasv3d.6
riotasv3d.7
Assertion
Ref Expression
riotasv3d
Distinct variable groups:   ,,   ,   ,   ,
Allowed substitution hints:   (,)   ()   (,)   (,)   ()   ()   (,)   (,)

Proof of Theorem riotasv3d
StepHypRef Expression
1 elex 2964 . 2
2 riotasv3d.7 . . . 4
32adantr 452 . . 3
4 riotasv3d.1 . . . . . 6
5 nfv 1629 . . . . . 6
6 riotasv3d.5 . . . . . . . . . 10
76imp 419 . . . . . . . . 9
87adantrl 697 . . . . . . . 8
9 riotasv3d.3 . . . . . . . . . . . 12
10 riotasv3d.6 . . . . . . . . . . . 12
119, 10riotasvd 6592 . . . . . . . . . . 11
1211impr 603 . . . . . . . . . 10
1312eqcomd 2441 . . . . . . . . 9
14 riotasv3d.4 . . . . . . . . 9
1513, 14syldan 457 . . . . . . . 8
168, 15mpbid 202 . . . . . . 7
1716exp45 598 . . . . . 6
184, 5, 17ralrimd 2794 . . . . 5
19 riotasv3d.2 . . . . . 6
20 r19.23t 2820 . . . . . 6
2119, 20syl 16 . . . . 5
2218, 21sylibd 206 . . . 4
2322imp 419 . . 3
243, 23mpd 15 . 2
251, 24sylan2 461 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652   wcel 1725  wral 2705  wrex 2706  cvv 2956  crio 6542 This theorem is referenced by:  cdlemefs32sn1aw  31211  cdleme43fsv1snlem  31217  cdleme41sn3a  31230  cdleme40m  31264  cdleme40n  31265  cdlemkid  31733  dihvalcqpre  32033 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 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 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-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-nel 2602  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-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-iota 5418  df-fun 5456  df-fv 5462  df-undef 6543  df-riota 6549
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