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Theorem ceqsralt 2882
 Description: Restricted quantifier version of ceqsalt 2881. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)
Assertion
Ref Expression
ceqsralt
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ceqsralt
StepHypRef Expression
1 df-ral 2619 . . . 4
2 eleq1 2413 . . . . . . . . 9
32pm5.32ri 619 . . . . . . . 8
43imbi1i 315 . . . . . . 7
5 impexp 433 . . . . . . 7
6 impexp 433 . . . . . . 7
74, 5, 63bitr3i 266 . . . . . 6
87albii 1566 . . . . 5
98a1i 10 . . . 4
101, 9syl5bb 248 . . 3
11 19.21v 1890 . . 3
1210, 11syl6bb 252 . 2
13 biimt 325 . . 3
14133ad2ant3 978 . 2
15 ceqsalt 2881 . 2
1612, 14, 153bitr2d 272 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wal 1540  wnf 1544   wceq 1642   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-ral 2619  df-v 2861 This theorem is referenced by:  ceqsralv  2886
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