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Theorem spc3egv 2943
 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 2869 . . . 4
2 elisset 2869 . . . 4
3 elisset 2869 . . . 4
41, 2, 33anim123i 1137 . . 3
5 eeeanv 1914 . . 3
64, 5sylibr 203 . 2
7 spc3egv.1 . . . . 5
87biimprcd 216 . . . 4
98eximdv 1622 . . 3
1092eximdv 1624 . 2
116, 10syl5com 26 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   w3a 934  wex 1541   wceq 1642   wcel 1710 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  spc3gv  2944
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