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Theorem tpid3g 3921
 Description: Closed theorem form of tpid3 3922. This proof was automatically generated from the virtual deduction proof tpid3gVD 29016 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 2968 . 2
2 3mix3 1129 . . . . . . 7
32a1i 11 . . . . . 6
4 abid 2426 . . . . . 6
53, 4syl6ibr 220 . . . . 5
6 dftp2 3856 . . . . . 6
76eleq2i 2502 . . . . 5
85, 7syl6ibr 220 . . . 4
9 eleq1 2498 . . . 4
108, 9mpbidi 209 . . 3
1110exlimdv 1647 . 2
121, 11mpd 15 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3o 936  wex 1551   wceq 1653   wcel 1726  cab 2424  ctp 3818 This theorem is referenced by:  en3lplem1  7672  en3lp  7674  nb3graprlem1  21462  en3lplem1VD  29017  en3lpVD  29019 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-pr 3823  df-tp 3824
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