Theorem eqbrtrri 3785

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

Step	Hyp	Ref	Expression
1		eqbrtrr.1	. . 3 |- A = B
2	1	eqcomi 2044	. 2 |- B = A
3		eqbrtrr.2	. 2 |- A R C
4	2, 3	eqbrtri 3783	1 |- B R C

Syntax hints:   = wceq 1243   class class class wbr 3764

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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765

This theorem is referenced by:  3brtr3i  3791  expnass  9357  sqrt2gt1lt2  9647