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Theorem elrabi 2718
 Description: Implication for the membership in a restricted class abstraction. (Contributed by Alexander van der Vekens, 31-Dec-2017.)
Assertion
Ref Expression
elrabi
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elrabi
StepHypRef Expression
1 clelab 2178 . . 3
2 eleq1 2116 . . . . . 6
32anbi1d 446 . . . . 5
43simprbda 369 . . . 4
54exlimiv 1505 . . 3
61, 5sylbi 118 . 2
7 df-rab 2332 . 2
86, 7eleq2s 2148 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wceq 1259  wex 1397   wcel 1409  cab 2042  crab 2327 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-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-rab 2332 This theorem is referenced by:  ordtriexmidlem  4273  ordtri2or2exmidlem  4279  onsucelsucexmidlem  4282  ordsoexmid  4314  reg3exmidlemwe  4331  acexmidlemcase  5535  genpelvl  6668  genpelvu  6669  nnindnn  7025  nnind  8006  ublbneg  8645
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