MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  oteq2d Unicode version

Theorem oteq2d 4025
Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1
Assertion
Ref Expression
oteq2d

Proof of Theorem oteq2d
StepHypRef Expression
1 oteq1d.1 . 2
2 oteq2 4022 . 2
31, 2syl 16 1
Colors of variables: wff set class
Syntax hints:  ->wi 4  =wceq 1654  <.cotp 3845
This theorem is referenced by:  oteq123d  4027  mapdh9a  32828  hdmap1eulem  32862  hdmapffval  32867  hdmapfval  32868  hdmapval2  32873
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 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
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 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-sn 3847  df-pr 3848  df-op 3850  df-ot 3851
  Copyright terms: Public domain W3C validator