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Theorem elabgt 2982
 Description: Membership in a class abstraction, using implicit substitution. (Closed theorem version of elabg 2986.) (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 2341 . . . . . . 7
2 eleq1 2413 . . . . . . 7
31, 2syl5bbr 250 . . . . . 6
43bibi1d 310 . . . . 5
54biimpd 198 . . . 4
65a2i 12 . . 3
76alimi 1559 . 2
8 nfcv 2489 . . . 4
9 nfab1 2491 . . . . . 6
109nfel2 2501 . . . . 5
11 nfv 1619 . . . . 5
1210, 11nfbi 1834 . . . 4
13 pm5.5 326 . . . 4
148, 12, 13spcgf 2934 . . 3
1514imp 418 . 2
167, 15sylan2 460 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wceq 1642   wcel 1710  cab 2339 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by: (None)
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