MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ceqsralt Unicode version

Theorem ceqsralt 3133
Description: Restricted quantifier version of ceqsalt 3132. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)
Assertion
Ref Expression
ceqsralt
Distinct variable groups:   ,   ,

Proof of Theorem ceqsralt
StepHypRef Expression
1 df-ral 2812 . . . 4
2 eleq1 2529 . . . . . . . . 9
32pm5.32ri 638 . . . . . . . 8
43imbi1i 325 . . . . . . 7
5 impexp 446 . . . . . . 7
6 impexp 446 . . . . . . 7
74, 5, 63bitr3i 275 . . . . . 6
87albii 1640 . . . . 5
98a1i 11 . . . 4
101, 9syl5bb 257 . . 3
11 19.21v 1729 . . 3
1210, 11syl6bb 261 . 2
13 biimt 335 . . 3
14133ad2ant3 1019 . 2
15 ceqsalt 3132 . 2
1612, 14, 153bitr2d 281 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  A.wral 2807
This theorem is referenced by:  ceqsralv  3138  cdleme32fva  36163
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-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-v 3111
  Copyright terms: Public domain W3C validator