Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dmtpop Structured version   Unicode version

Theorem dmtpop 5470
 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 4015 . . . 4
21dmeqi 5190 . . 3
3 dmun 5195 . . 3
4 dmsnop.1 . . . . 5
5 dmprop.1 . . . . 5
64, 5dmprop 5469 . . . 4
7 dmtpop.1 . . . . 5
87dmsnop 5468 . . . 4
96, 8uneq12i 3638 . . 3
102, 3, 93eqtri 2474 . 2
11 df-tp 4015 . 2
1210, 11eqtr4i 2473 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1381   wcel 1802  cvv 3093   cun 3456  csn 4010  cpr 4012  ctp 4014  cop 4016   cdm 4985 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-9 1806  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419  ax-sep 4554  ax-nul 4562  ax-pr 4672 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-rab 2800  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-sn 4011  df-pr 4013  df-tp 4015  df-op 4017  df-br 4434  df-dm 4995 This theorem is referenced by:  fntp  5630
 Copyright terms: Public domain W3C validator