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Theorem elab3gf 3079
 Description: Membership in a class abstraction, with a weaker antecedent than elabgf 3072. (Contributed by NM, 6-Sep-2011.)
Hypotheses
Ref Expression
elab3gf.1
elab3gf.2
elab3gf.3
Assertion
Ref Expression
elab3gf

Proof of Theorem elab3gf
StepHypRef Expression
1 elab3gf.1 . . . . 5
2 elab3gf.2 . . . . 5
3 elab3gf.3 . . . . 5
41, 2, 3elabgf 3072 . . . 4
54ibi 233 . . 3
6 pm2.21 102 . . 3
75, 6impbid2 196 . 2
81, 2, 3elabgf 3072 . 2
97, 8ja 155 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wnf 1553   wceq 1652   wcel 1725  cab 2421  wnfc 2558 This theorem is referenced by:  elab3g  3080 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950
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