Theorem breqtrri 3810

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

Step	Hyp	Ref	Expression
1		breqtrr.1	. 2 |- A R B
2		breqtrr.2	. . 3 |- C = B
3	2	eqcomi 2085	. 2 |- B = C
4	1, 3	breqtri 3808	1 |- A R C

Syntax hints:   = wceq 1284   class class class wbr 3785

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-br 3786

This theorem is referenced by:  3brtr4i  3813  ensn1  6299  0lt1sr  6942  0le2  8129  2pos  8130  3pos  8133  4pos  8136  5pos  8139  6pos  8140  7pos  8141  8pos  8142  9pos  8143  1lt2  8201  2lt3  8202  3lt4  8204  4lt5  8207  5lt6  8211  6lt7  8216  7lt8  8222  8lt9  8229  nn0le2xi  8338  numltc  8502  declti  8514  sqge0i  9562  faclbnd2  9669  3dvdsdec  10264  n2dvdsm1  10313  n2dvds3  10315  ex-fl  10563