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Theorem ceqsex2 2994
 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 941 . . . . 5
21exbii 1593 . . . 4
3 19.42v 1929 . . . 4
42, 3bitri 242 . . 3
54exbii 1593 . 2
6 nfv 1630 . . . . 5
7 ceqsex2.1 . . . . 5
86, 7nfan 1847 . . . 4
98nfex 1866 . . 3
10 ceqsex2.3 . . 3
11 ceqsex2.5 . . . . 5
1211anbi2d 686 . . . 4
1312exbidv 1637 . . 3
149, 10, 13ceqsex 2992 . 2
15 ceqsex2.2 . . 3
16 ceqsex2.4 . . 3
17 ceqsex2.6 . . 3
1815, 16, 17ceqsex 2992 . 2
195, 14, 183bitri 264 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937  wex 1551  wnf 1554   wceq 1653   wcel 1726  cvv 2958 This theorem is referenced by:  ceqsex2v  2995 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-v 2960
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