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Theorem elab3gf 2715
 Description: Membership in a class abstraction, with a weaker antecedent than elabgf 2708. (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 2708 . . 3
54ibi 169 . 2
61, 2, 3elabgf 2708 . . . 4
76imim2i 12 . . 3
8 bi2 125 . . 3
97, 8syli 37 . 2
105, 9impbid2 135 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102   wceq 1259  wnf 1365   wcel 1409  cab 2042  wnfc 2181 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576 This theorem is referenced by:  elab3g  2716
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