Theorem eqbrtrri 4082

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 2211	. 2 |- B = A
3		eqbrtrr.2	. 2 |- A R C
4	2, 3	eqbrtri 4080	1 |- B R C

Syntax hints:   = wceq 1373   class class class wbr 4059

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-sn 3649  df-pr 3650  df-op 3652  df-br 4060

This theorem is referenced by:  3brtr3i  4088  dju1p1e2  7336  expnass  10827  sqrt2gt1lt2  11475  cos1bnd  12185  cos2bnd  12186  infpn2  12942  2strstr1g  13069  coseq00topi  15422  pigt3  15431