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Theorem breqtrri 3780
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtrr.1  R
breqtrr.2  C
Assertion
Ref Expression
breqtrri  R C

Proof of Theorem breqtrri
StepHypRef Expression
1 breqtrr.1 . 2  R
2 breqtrr.2 . . 3  C
32eqcomi 2041 . 2  C
41, 3breqtri 3778 1  R C
Colors of variables: wff set class
Syntax hints:   wceq 1242   class class class wbr 3755
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756
This theorem is referenced by:  3brtr4i  3783  ensn1  6212  0lt1sr  6693  0le2  7786  2pos  7787  3pos  7790  4pos  7792  5pos  7794  6pos  7795  7pos  7796  8pos  7797  9pos  7798  10pos  7799  1lt2  7864  2lt3  7865  3lt4  7867  4lt5  7870  5lt6  7874  6lt7  7879  7lt8  7885  8lt9  7892  9lt10  7900  nn0le2xi  8008  numltc  8163  declti  8168  sqge0i  8993
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