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Theorem spc3egv 2638
Description: Existential specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.)
Hypothesis
Ref Expression
spc3egv.1  C
Assertion
Ref Expression
spc3egv  V  W  C  X
Distinct variable groups:   ,,,   ,,,   , C,,   ,,,
Allowed substitution hints:   (,,)    V(,,)    W(,,)    X(,,)

Proof of Theorem spc3egv
StepHypRef Expression
1 elisset 2562 . . . 4  V
2 elisset 2562 . . . 4  W
3 elisset 2562 . . . 4  C  X  C
41, 2, 33anim123i 1088 . . 3  V  W  C  X  C
5 eeeanv 1805 . . 3  C  C
64, 5sylibr 137 . 2  V  W  C  X  C
7 spc3egv.1 . . . . 5  C
87biimprcd 149 . . . 4  C
98eximdv 1757 . . 3  C
1092eximdv 1759 . 2  C
116, 10syl5com 26 1  V  W  C  X
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   w3a 884   wceq 1242  wex 1378   wcel 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by: (None)
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