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Theorem spc3gv 3141
 Description: Specialization with three 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 296 . . . 4
32spc3egv 3140 . . 3
4 exnal 1701 . . . . . . 7
54exbii 1720 . . . . . 6
6 exnal 1701 . . . . . 6
75, 6bitri 253 . . . . 5
87exbii 1720 . . . 4
9 exnal 1701 . . . 4
108, 9bitr2i 254 . . 3
113, 10syl6ibr 231 . 2
1211con4d 109 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   w3a 986  wal 1444   wceq 1446  wex 1665   wcel 1889 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-v 3049 This theorem is referenced by:  funopg  5617  pslem  16464  dirtr  16494  mclsax  30219  fununiq  30422
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