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Theorem elab3gf 2858
 Description: Membership in a class abstraction, with a weaker antecedent than elabgf 2850. (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 . . . 4
2 elab3gf.2 . . . 4
3 elab3gf.3 . . . 4
41, 2, 3elabgf 2850 . . 3
54ibi 175 . 2
61, 2, 3elabgf 2850 . . . 4
76imim2i 12 . . 3
8 biimpr 129 . . 3
97, 8syli 37 . 2
105, 9impbid2 142 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332  wnf 1437   wcel 2125  cab 2140  wnfc 2283 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711 This theorem is referenced by:  elab3g  2859
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