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Theorem spc3gv 3033
 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 286 . . . 4
32spc3egv 3032 . . 3
4 exnal 1583 . . . . . . 7
54exbii 1592 . . . . . 6
6 exnal 1583 . . . . . 6
75, 6bitri 241 . . . . 5
87exbii 1592 . . . 4
9 exnal 1583 . . . 4
108, 9bitr2i 242 . . 3
113, 10syl6ibr 219 . 2
1211con4d 99 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725 This theorem is referenced by:  funopg  5477  pslem  14630  dirtr  14673  fununiq  25386 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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