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Theorem spc3egv 3198
 Description: Existential specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.)
Hypothesis
Ref Expression
spc3egv.1
Assertion
Ref Expression
spc3egv
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem spc3egv
StepHypRef Expression
1 elisset 3120 . . . 4
2 elisset 3120 . . . 4
3 elisset 3120 . . . 4
41, 2, 33anim123i 1181 . . 3
5 eeeanv 1989 . . 3
64, 5sylibr 212 . 2
7 spc3egv.1 . . . . 5
87biimprcd 225 . . . 4
98eximdv 1710 . . 3
1092eximdv 1712 . 2
116, 10syl5com 30 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818 This theorem is referenced by:  spc3gv  3199  dihjatcclem4  37148 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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