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Theorem ceqsex3v 2994
 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:   ,,,   ,,,   ,,,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,)

Proof of Theorem ceqsex3v
StepHypRef Expression
1 anass 631 . . . . . 6
2 3anass 940 . . . . . . 7
32anbi1i 677 . . . . . 6
4 df-3an 938 . . . . . . 7
54anbi2i 676 . . . . . 6
61, 3, 53bitr4i 269 . . . . 5
762exbii 1593 . . . 4
8 19.42vv 1930 . . . 4
97, 8bitri 241 . . 3
109exbii 1592 . 2
11 ceqsex3v.1 . . . 4
12 ceqsex3v.4 . . . . . 6
13123anbi3d 1260 . . . . 5
14132exbidv 1638 . . . 4
1511, 14ceqsexv 2991 . . 3
16 ceqsex3v.2 . . . 4
17 ceqsex3v.3 . . . 4
18 ceqsex3v.5 . . . 4
19 ceqsex3v.6 . . . 4
2016, 17, 18, 19ceqsex2v 2993 . . 3
2115, 20bitri 241 . 2
2210, 21bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cvv 2956 This theorem is referenced by:  ceqsex6v  2996 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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