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Theorem spc3egv 2749
 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 2672 . . . 4
2 elisset 2672 . . . 4
3 elisset 2672 . . . 4
41, 2, 33anim123i 1149 . . 3
5 eeeanv 1883 . . 3
64, 5sylibr 133 . 2
7 spc3egv.1 . . . . 5
87biimprcd 159 . . . 4
98eximdv 1834 . . 3
1092eximdv 1836 . 2
116, 10syl5com 29 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   w3a 945   wceq 1314  wex 1451   wcel 1463 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-v 2660 This theorem is referenced by: (None)
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