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Theorem spc3egv 3040
 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:   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,,)

Proof of Theorem spc3egv
StepHypRef Expression
1 elisset 2966 . . . 4
2 elisset 2966 . . . 4
3 elisset 2966 . . . 4
41, 2, 33anim123i 1139 . . 3
5 eeeanv 1938 . . 3
64, 5sylibr 204 . 2
7 spc3egv.1 . . . . 5
87biimprcd 217 . . . 4
98eximdv 1632 . . 3
1092eximdv 1634 . 2
116, 10syl5com 28 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936  wex 1550   wceq 1652   wcel 1725 This theorem is referenced by:  spc3gv  3041  dihjatcclem4  32219 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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