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Theorem spc3gv 2886
 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 2885 . . 3
4 exnal 1564 . . . . . . 7
54exbii 1572 . . . . . 6
6 exnal 1564 . . . . . 6
75, 6bitri 240 . . . . 5
87exbii 1572 . . . 4
9 exnal 1564 . . . 4
108, 9bitr2i 241 . . 3
113, 10syl6ibr 218 . 2
1211con4d 97 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   w3a 934  wal 1530  wex 1531   wceq 1632   wcel 1696 This theorem is referenced by:  funopg  5302  pslem  14331  dirtr  14374  fununiq  24197  preotr2  25338 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-v 2803
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