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Theorem breqtrri 4462
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999.)
Hypotheses
Ref Expression
breqtrr.1  |-  A R B
breqtrr.2  |-  C  =  B
Assertion
Ref Expression
breqtrri  |-  A R C

Proof of Theorem breqtrri
StepHypRef Expression
1 breqtrr.1 . 2  |-  A R B
2 breqtrr.2 . . 3  |-  C  =  B
32eqcomi 2456 . 2  |-  B  =  C
41, 3breqtri 4460 1  |-  A R C
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383   class class class wbr 4437
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-br 4438
This theorem is referenced by:  3brtr4i  4465  ensn1  7581  1sdom2  7720  pm110.643ALT  8561  infmap2  8601  0lt1sr  9475  0le2  10633  2pos  10634  3pos  10636  4pos  10638  5pos  10640  6pos  10641  7pos  10642  8pos  10643  9pos  10644  10pos  10645  1lt2  10709  2lt3  10710  3lt4  10712  4lt5  10715  5lt6  10719  6lt7  10724  7lt8  10730  8lt9  10737  9lt10  10745  nn0le2xi  10854  numltc  11006  declti  11011  xlemul1a  11491  sqge0i  12237  faclbnd2  12351  cats1fv  12806  ege2le3  13807  cos2bnd  13905  divalglem2  14035  pockthi  14407  dec2dvds  14531  prmlem1  14575  prmlem2  14587  1259prm  14600  2503prm  14604  4001prm  14609  vitalilem5  21999  dveflem  22358  tangtx  22876  sinq12ge0  22879  cxpge0  23042  asin1  23203  birthday  23262  ppiub  23457  bposlem4  23540  bposlem5  23541  bposlem7  23543  lgsdir2lem2  23577  ex-fl  25146  ex-ind-dvds  25148  siilem2  25745  normlem6  26010  normlem7  26011  cm2mi  26522  pjnormi  26617  unierri  27001  lgamgulmlem4  28552  ftc1anclem5  30070  fdc  30214  pellfundgt1  30795  jm2.27dlem2  30928  stoweidlem13  31749  sqwvfoura  31965  sqwvfourb  31966  fourierswlem  31967  taupi  37573
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