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Theorem elssabg 4355
 Description: Membership in a class abstraction involving a subset. Unlike elabg 3083, does not have to be a set. (Contributed by NM, 29-Aug-2006.)
Hypothesis
Ref Expression
elssabg.1
Assertion
Ref Expression
elssabg
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elssabg
StepHypRef Expression
1 ssexg 4349 . . . 4
21expcom 425 . . 3
4 sseq1 3369 . . . 4
5 elssabg.1 . . . 4
64, 5anbi12d 692 . . 3
76elab3g 3088 . 2
83, 7syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  cab 2422  cvv 2956   wss 3320 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-ss 3334
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