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Theorem spc3gv 2944
 Description: Specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.)
Hypothesis
Ref Expression
spc3egv.1
Assertion
Ref Expression
spc3gv
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,,)

Proof of Theorem spc3gv
StepHypRef Expression
1 spc3egv.1 . . . . 5
21notbid 285 . . . 4
32spc3egv 2943 . . 3
4 exnal 1574 . . . . . . 7
54exbii 1582 . . . . . 6
6 exnal 1574 . . . . . 6
75, 6bitri 240 . . . . 5
87exbii 1582 . . . 4
9 exnal 1574 . . . 4
108, 9bitr2i 241 . . 3
113, 10syl6ibr 218 . 2
1211con4d 97 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   w3a 934  wal 1540  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:  fununiq  5517
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