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Theorem eqbrtrri 4060
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtrr.1  |-  A  =  B
eqbrtrr.2  |-  A R C
Assertion
Ref Expression
eqbrtrri  |-  B R C

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3  |-  A  =  B
21eqcomi 2300 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 4058 1  |-  B R C
Colors of variables: wff set class
Syntax hints:    = wceq 1632   class class class wbr 4039
This theorem is referenced by:  3brtr3i  4066  expnass  11224  faclbnd4lem1  11322  sqr2gt1lt2  11776  cos1bnd  12483  cos2bnd  12484  prdsvalstr  13369  ovolre  18900  pige3  19901  atan1  20240  log2ublem1  20258  sqrlim  20283  bposlem8  20546  chebbnd1  20637  norm-ii-i  21732  nmopadji  22686  unierri  22700  konigsberg  23926  stoweidlem26  27878  wallispilem5  27921
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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