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Theorem ceqsex2 2895
 Description: Elimination of two existential quantifiers, using implicit substitution. (Contributed by Scott Fenton, 7-Jun-2006.)
Hypotheses
Ref Expression
ceqsex2.1
ceqsex2.2
ceqsex2.3
ceqsex2.4
ceqsex2.5
ceqsex2.6
Assertion
Ref Expression
ceqsex2
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem ceqsex2
StepHypRef Expression
1 3anass 938 . . . . 5
21exbii 1582 . . . 4
3 19.42v 1905 . . . 4
42, 3bitri 240 . . 3
54exbii 1582 . 2
6 nfv 1619 . . . . 5
7 ceqsex2.1 . . . . 5
86, 7nfan 1824 . . . 4
98nfex 1843 . . 3
10 ceqsex2.3 . . 3
11 ceqsex2.5 . . . . 5
1211anbi2d 684 . . . 4
1312exbidv 1626 . . 3
149, 10, 13ceqsex 2893 . 2
15 ceqsex2.2 . . 3
16 ceqsex2.4 . . 3
17 ceqsex2.6 . . 3
1815, 16, 17ceqsex 2893 . 2
195, 14, 183bitri 262 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wex 1541  wnf 1544   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:  ceqsex2v  2896
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