Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  oteq1d Structured version   Unicode version

Theorem oteq1d 4214
 Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1
Assertion
Ref Expression
oteq1d

Proof of Theorem oteq1d
StepHypRef Expression
1 oteq1d.1 . 2
2 oteq1 4211 . 2
31, 2syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1383  cotp 4022 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-ot 4023 This theorem is referenced by:  oteq123d  4217  msrfval  28875  msrid  28883  elmsta  28886  mthmpps  28920  hdmapfval  37432
 Copyright terms: Public domain W3C validator