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

Theorem eqbrtri 3958
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtr.1
eqbrtr.2
Assertion
Ref Expression
eqbrtri

Proof of Theorem eqbrtri
StepHypRef Expression
1 eqbrtr.2 . 2
2 eqbrtr.1 . . 3
32breq1i 3945 . 2
41, 3mpbir 145 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   class class class wbr 3938 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939 This theorem is referenced by:  eqbrtrri  3960  3brtr4i  3967  exmidonfinlem  7069  neg1lt0  8872  halflt1  8981  3halfnz  9192  declei  9261  numlti  9262  faclbnd3  10541  geo2lim  11337  0.999...  11342  geoihalfsum  11343  tan0  11494  cos2bnd  11523  sin4lt0  11529  eirraplem  11539  1nprm  11851  znnen  11967  tan4thpi  12990  ex-fl  13128  trilpolemisumle  13427
 Copyright terms: Public domain W3C validator