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Theorem elrab3t 3256
 Description: Membership in a restricted class abstraction, using implicit substitution. (Closed theorem version of elrab3 3258.) (Contributed by Thierry Arnoux, 31-Aug-2017.)
Assertion
Ref Expression
elrab3t
Distinct variable groups:   ,   ,   ,

Proof of Theorem elrab3t
StepHypRef Expression
1 df-rab 2816 . . 3
21eleq2i 2535 . 2
3 simpr 461 . . 3
4 nfa1 1897 . . . . 5
5 nfv 1707 . . . . 5
64, 5nfan 1928 . . . 4
7 simpl 457 . . . . . 6
8719.21bi 1869 . . . . 5
9 eleq1 2529 . . . . . . . . . 10
109biimparc 487 . . . . . . . . 9
1110biantrurd 508 . . . . . . . 8
1211bibi1d 319 . . . . . . 7
1312pm5.74da 687 . . . . . 6
1413adantl 466 . . . . 5
158, 14mpbid 210 . . . 4
166, 15alrimi 1877 . . 3
17 elabgt 3243 . . 3
183, 16, 17syl2anc 661 . 2
192, 18syl5bb 257 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811 This theorem is referenced by:  f1oresrab  6063 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111
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