Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  relin1 Structured version   Unicode version

Theorem relin1 5110
 Description: The intersection with a relation is a relation. (Contributed by NM, 16-Aug-1994.)
Assertion
Ref Expression
relin1

Proof of Theorem relin1
StepHypRef Expression
1 inss1 3703 . 2
2 relss 5080 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   cin 3460   wss 3461   wrel 4994 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-an 371  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-v 3097  df-in 3468  df-ss 3475  df-rel 4996 This theorem is referenced by:  inopab  5123  idsset  29515  dihmeetlem1N  36757  dihglblem5apreN  36758  dihmeetlem4preN  36773  dihmeetlem13N  36786
 Copyright terms: Public domain W3C validator