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Theorem tpid3g 4086
 Description: Closed theorem form of tpid3 4087. This proof was automatically generated from the virtual deduction proof tpid3gVD 37232 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 3056 . 2
2 3mix3 1178 . . . . . . 7
32a1i 11 . . . . . 6
4 abid 2438 . . . . . 6
53, 4syl6ibr 231 . . . . 5
6 dftp2 4017 . . . . . 6
76eleq2i 2520 . . . . 5
85, 7syl6ibr 231 . . . 4
9 eleq1 2516 . . . 4
108, 9mpbidi 220 . . 3
1110exlimdv 1778 . 2
121, 11mpd 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3o 983   wceq 1443  wex 1662   wcel 1886  cab 2436  ctp 3971 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 985  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-v 3046  df-un 3408  df-sn 3968  df-pr 3970  df-tp 3972 This theorem is referenced by:  tpnzd  4093  f1dom3fv3dif  6166  f1dom3el3dif  6167  en3lplem1  8116  en3lp  8118  nb3graprlem1  25172  en3lplem1VD  37233  en3lpVD  37235  etransclem48OLD  38141  etransclem48  38142  nb3grprlem1  39437  cplgr3v  39485
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