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Theorem elabgt 3243
Description: Membership in a class abstraction, using implicit substitution. (Closed theorem version of elabg 3247.) (Contributed by NM, 7-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
elabgt
Distinct variable groups:   ,   ,

Proof of Theorem elabgt
StepHypRef Expression
1 abid 2444 . . . . . . 7
2 eleq1 2529 . . . . . . 7
31, 2syl5bbr 259 . . . . . 6
43bibi1d 319 . . . . 5
54biimpd 207 . . . 4
65a2i 13 . . 3
76alimi 1633 . 2
8 nfcv 2619 . . . 4
9 nfab1 2621 . . . . . 6
109nfel2 2637 . . . . 5
11 nfv 1707 . . . . 5
1210, 11nfbi 1934 . . . 4
13 pm5.5 336 . . . 4
148, 12, 13spcgf 3189 . . 3
1514imp 429 . 2
167, 15sylan2 474 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442
This theorem is referenced by:  elrab3t  3256  abfmpeld  27492  abfmpel  27493  dfrtrcl2  29071
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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