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Theorem ceqsex3v 2897
 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 630 . . . . . 6
2 3anass 938 . . . . . . 7
32anbi1i 676 . . . . . 6
4 df-3an 936 . . . . . . 7
54anbi2i 675 . . . . . 6
61, 3, 53bitr4i 268 . . . . 5
762exbii 1583 . . . 4
8 19.42vv 1907 . . . 4
97, 8bitri 240 . . 3
109exbii 1582 . 2
11 ceqsex3v.1 . . . 4
12 ceqsex3v.4 . . . . . 6
13123anbi3d 1258 . . . . 5
14132exbidv 1628 . . . 4
1511, 14ceqsexv 2894 . . 3
16 ceqsex3v.2 . . . 4
17 ceqsex3v.3 . . . 4
18 ceqsex3v.5 . . . 4
19 ceqsex3v.6 . . . 4
2016, 17, 18, 19ceqsex2v 2896 . . 3
2115, 20bitri 240 . 2
2210, 21bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wex 1541   wceq 1642   wcel 1710  cvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  ceqsex6v  2899
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