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Theorem ceqsex2 3072
 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 1011 . . . . 5
21exbii 1726 . . . 4
3 19.42v 1842 . . . 4
42, 3bitri 257 . . 3
54exbii 1726 . 2
6 nfv 1769 . . . . 5
7 ceqsex2.1 . . . . 5
86, 7nfan 2031 . . . 4
98nfex 2050 . . 3
10 ceqsex2.3 . . 3
11 ceqsex2.5 . . . . 5
1211anbi2d 718 . . . 4
1312exbidv 1776 . . 3
149, 10, 13ceqsex 3069 . 2
15 ceqsex2.2 . . 3
16 ceqsex2.4 . . 3
17 ceqsex2.6 . . 3
1815, 16, 17ceqsex 3069 . 2
195, 14, 183bitri 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   w3a 1007   wceq 1452  wex 1671  wnf 1675   wcel 1904  cvv 3031 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033 This theorem is referenced by:  ceqsex2v  3073
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