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Theorem elabgt 2924
 Description: Membership in a class abstraction, using implicit substitution. (Closed theorem version of elabg 2928.) (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 2284 . . . . . . 7
2 eleq1 2356 . . . . . . 7
31, 2syl5bbr 250 . . . . . 6
43bibi1d 310 . . . . 5
54biimpd 198 . . . 4
65a2i 12 . . 3
76alimi 1549 . 2
8 nfcv 2432 . . . 4
9 nfab1 2434 . . . . . 6
109nfel2 2444 . . . . 5
11 nfv 1609 . . . . 5
1210, 11nfbi 1784 . . . 4
13 pm5.5 326 . . . 4
148, 12, 13spcgf 2876 . . 3
1514imp 418 . 2
167, 15sylan2 460 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530   wceq 1632   wcel 1696  cab 2282 This theorem is referenced by:  abfmpeld  23233  abfmpel  23234  esumc  23445  dfrtrcl2  24060  eqintg  25064 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803
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