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Theorem ceqsex3v 3149
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 977 . . . . . . 7
32anbi1i 695 . . . . . 6
4 df-3an 975 . . . . . . 7
54anbi2i 694 . . . . . 6
61, 3, 53bitr4i 277 . . . . 5
762exbii 1668 . . . 4
8 19.42vv 1777 . . . 4
97, 8bitri 249 . . 3
109exbii 1667 . 2
11 ceqsex3v.1 . . . 4
12 ceqsex3v.4 . . . . . 6
13123anbi3d 1305 . . . . 5
14132exbidv 1716 . . . 4
1511, 14ceqsexv 3146 . . 3
16 ceqsex3v.2 . . . 4
17 ceqsex3v.3 . . . 4
18 ceqsex3v.5 . . . 4
19 ceqsex3v.6 . . . 4
2016, 17, 18, 19ceqsex2v 3148 . . 3
2115, 20bitri 249 . 2
2210, 21bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109
This theorem is referenced by:  ceqsex6v  3151
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-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-v 3111
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