Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqbrtrri Unicode version

Theorem eqbrtrri 3951
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtrr.1
eqbrtrr.2
Assertion
Ref Expression
eqbrtrri

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3
21eqcomi 2143 . 2
3 eqbrtrr.2 . 2
42, 3eqbrtri 3949 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   class class class wbr 3929 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930 This theorem is referenced by:  3brtr3i  3957  dju1p1e2  7053  expnass  10405  sqrt2gt1lt2  10828  cos1bnd  11472  cos2bnd  11473  2strstr1g  12071  coseq00topi  12932  pigt3  12941
 Copyright terms: Public domain W3C validator