Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  spc3gv Unicode version

Theorem spc3gv 3199
 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:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem spc3gv
StepHypRef Expression
1 spc3egv.1 . . . . 5
21notbid 294 . . . 4
32spc3egv 3198 . . 3
4 exnal 1648 . . . . . . 7
54exbii 1667 . . . . . 6
6 exnal 1648 . . . . . 6
75, 6bitri 249 . . . . 5
87exbii 1667 . . . 4
9 exnal 1648 . . . 4
108, 9bitr2i 250 . . 3
113, 10syl6ibr 227 . 2
1211con4d 105 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\w3a 973  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818 This theorem is referenced by:  funopg  5625  pslem  15836  dirtr  15866  mclsax  28929  fununiq  29200 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
 Copyright terms: Public domain W3C validator