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Theorem elabgt 3157
 Description: Membership in a class abstraction, using implicit substitution. (Closed theorem version of elabg 3161.) (Contributed by NM, 7-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
elabgt
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elabgt
StepHypRef Expression
1 abid 2416 . . . . . . 7
2 eleq1 2494 . . . . . . 7
31, 2syl5bbr 262 . . . . . 6
43bibi1d 320 . . . . 5
54biimpd 210 . . . 4
65a2i 14 . . 3
76alimi 1678 . 2
8 nfcv 2569 . . . 4
9 nfab1 2571 . . . . . 6
109nfel2 2585 . . . . 5
11 nfv 1755 . . . . 5
1210, 11nfbi 1994 . . . 4
13 pm5.5 337 . . . 4
148, 12, 13spcgf 3104 . . 3
1514imp 430 . 2
167, 15sylan2 476 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wceq 1437   wcel 1872  cab 2414 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 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-v 3024 This theorem is referenced by:  elrab3t  3170  dfrtrcl2  13069  abfmpeld  28199  abfmpel  28200  dftrcl3  36225  dfrtrcl3  36238
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