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Theorem ceqsex3v 3092
Description: Elimination of three existential quantifiers, using implicit substitution. (Contributed by NM, 16-Aug-2011.)
Hypotheses
Ref Expression
ceqsex3v.1
ceqsex3v.2
ceqsex3v.3
ceqsex3v.4
ceqsex3v.5
ceqsex3v.6
Assertion
Ref Expression
ceqsex3v
Distinct variable groups:   , , ,   , , ,   , , ,   ,   ,   ,

Proof of Theorem ceqsex3v
StepHypRef Expression
1 anass 649 . . . . . 6
2 3anass 969 . . . . . . 7
32anbi1i 695 . . . . . 6
4 df-3an 967 . . . . . . 7
54anbi2i 694 . . . . . 6
61, 3, 53bitr4i 277 . . . . 5
762exbii 1636 . . . 4
8 19.42vv 1927 . . . 4
97, 8bitri 249 . . 3
109exbii 1635 . 2
11 ceqsex3v.1 . . . 4
12 ceqsex3v.4 . . . . . 6
13123anbi3d 1296 . . . . 5
14132exbidv 1683 . . . 4
1511, 14ceqsexv 3089 . . 3
16 ceqsex3v.2 . . . 4
17 ceqsex3v.3 . . . 4
18 ceqsex3v.5 . . . 4
19 ceqsex3v.6 . . . 4
2016, 17, 18, 19ceqsex2v 3091 . . 3
2115, 20bitri 249 . 2
2210, 21bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 965  =wceq 1370  E.wex 1587  e.wcel 1757   cvv 3052
This theorem is referenced by:  ceqsex6v  3094
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-10 1776  ax-11 1781  ax-12 1793  ax-ext 2429
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1702  df-clab 2436  df-cleq 2442  df-clel 2445  df-v 3054
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