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Theorem ceqsex2 2594
 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 889 . . . . 5
21exbii 1496 . . . 4
3 19.42v 1786 . . . 4
42, 3bitri 173 . . 3
54exbii 1496 . 2
6 nfv 1421 . . . . 5
7 ceqsex2.1 . . . . 5
86, 7nfan 1457 . . . 4
98nfex 1528 . . 3
10 ceqsex2.3 . . 3
11 ceqsex2.5 . . . . 5
1211anbi2d 437 . . . 4
1312exbidv 1706 . . 3
149, 10, 13ceqsex 2592 . 2
15 ceqsex2.2 . . 3
16 ceqsex2.4 . . 3
17 ceqsex2.6 . . 3
1815, 16, 17ceqsex 2592 . 2
195, 14, 183bitri 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   w3a 885   wceq 1243  wnf 1349  wex 1381   wcel 1393  cvv 2557 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by:  ceqsex2v  2595
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