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Theorem breqtrri 4064
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
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 2300 . 2  |-  B  =  C
41, 3breqtri 4062 1  |-  A R C
Colors of variables: wff set class
Syntax hints:    = wceq 1632   class class class wbr 4039
This theorem is referenced by:  3brtr4i  4067  ensn1  6941  1sdom2  7077  pm110.643ALT  7820  infmap2  7860  0lt1sr  8733  2pos  9844  3pos  9846  4pos  9848  5pos  9849  6pos  9850  7pos  9851  8pos  9852  9pos  9853  10pos  9854  1lt2  9902  2lt3  9903  3lt4  9905  4lt5  9908  5lt6  9912  6lt7  9917  7lt8  9923  8lt9  9930  9lt10  9938  nn0le2xi  10031  numltc  10160  declti  10165  xlemul1a  10624  sqge0i  11207  faclbnd2  11320  cats1fv  11525  ege2le3  12387  cos2bnd  12484  divalglem2  12610  pockthi  12970  dec2dvds  13094  prmlem1  13125  prmlem2  13137  1259prm  13150  2503prm  13154  4001prm  13159  vitalilem5  18983  dveflem  19342  tangtx  19889  sinq12ge0  19892  cxpge0  20046  asin1  20206  birthday  20265  ppiub  20459  bposlem4  20542  bposlem5  20543  bposlem7  20545  lgsdir2lem2  20579  ex-fl  20850  siilem2  21446  normlem6  21710  normlem7  21711  cm2mi  22221  pjnormi  22316  unierri  22700  fdc  26558  pellfundgt1  27071  jm2.27dlem2  27206  stoweidlem13  27865
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040
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