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Theorem dmtpop 5349
 Description: The domain of an unordered triple of ordered pairs. (Contributed by NM, 14-Sep-2011.)
Hypotheses
Ref Expression
dmsnop.1
dmprop.1
dmtpop.1
Assertion
Ref Expression
dmtpop

Proof of Theorem dmtpop
StepHypRef Expression
1 df-tp 3824 . . . 4
21dmeqi 5074 . . 3
3 dmun 5079 . . 3
4 dmsnop.1 . . . . 5
5 dmprop.1 . . . . 5
64, 5dmprop 5348 . . . 4
7 dmtpop.1 . . . . 5
87dmsnop 5347 . . . 4
96, 8uneq12i 3501 . . 3
102, 3, 93eqtri 2462 . 2
11 df-tp 3824 . 2
1210, 11eqtr4i 2461 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  cvv 2958   cun 3320  csn 3816  cpr 3817  ctp 3818  cop 3819   cdm 4881 This theorem is referenced by:  fntp  5510 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  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-ne 2603  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-br 4216  df-dm 4891
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