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Theorem spc3egv 3170
 Description: Existential specialization with three 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 3091 . . . 4
2 elisset 3091 . . . 4
3 elisset 3091 . . . 4
41, 2, 33anim123i 1190 . . 3
5 eeeanv 2048 . . 3
64, 5sylibr 215 . 2
7 spc3egv.1 . . . . 5
87biimprcd 228 . . . 4
98eximdv 1758 . . 3
1092eximdv 1760 . 2
116, 10syl5com 31 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   w3a 982   wceq 1437  wex 1657   wcel 1872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-v 3082 This theorem is referenced by:  spc3gv  3171  dihjatcclem4  34958
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