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Theorem tpid3g 3511
 Description: Closed theorem form of tpid3 3512. (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 2585 . 2
2 3mix3 1086 . . . . . . 7
32a1i 9 . . . . . 6
4 abid 2044 . . . . . 6
53, 4syl6ibr 155 . . . . 5
6 dftp2 3447 . . . . . 6
76eleq2i 2120 . . . . 5
85, 7syl6ibr 155 . . . 4
9 eleq1 2116 . . . 4
108, 9mpbidi 144 . . 3
1110exlimdv 1716 . 2
121, 11mpd 13 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3o 895   wceq 1259  wex 1397   wcel 1409  cab 2042  ctp 3405 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3or 897  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-tp 3411 This theorem is referenced by: (None)
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