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Theorem tpid3g 4145
 Description: Closed theorem form of tpid3 4146. This proof was automatically generated from the virtual deduction proof tpid3gVD 33642 using a translation program. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
tpid3g

Proof of Theorem tpid3g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elisset 3120 . 2
2 3mix3 1167 . . . . . . 7
32a1i 11 . . . . . 6
4 abid 2444 . . . . . 6
53, 4syl6ibr 227 . . . . 5
6 dftp2 4075 . . . . . 6
76eleq2i 2535 . . . . 5
85, 7syl6ibr 227 . . . 4
9 eleq1 2529 . . . 4
108, 9mpbidi 216 . . 3
1110exlimdv 1724 . 2
121, 11mpd 15 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  \/w3o 972  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  {ctp 4033 This theorem is referenced by:  tpnzd  4152  f1dom3fv3dif  6175  f1dom3el3dif  6176  en3lplem1  8052  en3lp  8054  nb3graprlem1  24451  etransclem48  32065  en3lplem1VD  33643  en3lpVD  33645 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-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-sn 4030  df-pr 4032  df-tp 4034
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