Theorem eqbrtrri 4134

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 2238	. 2 |- B = A
3		eqbrtrr.2	. 2 |- A R C
4	2, 3	eqbrtri 4132	1 |- B R C

Syntax hints:   = wceq 1398   class class class wbr 4111

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-un 3217  df-sn 3697  df-pr 3698  df-op 3700  df-br 4112

This theorem is referenced by:  3brtr3i  4140  dju1p1e2  7502  expnass  11011  sqrt2gt1lt2  11738  cos1bnd  12449  cos2bnd  12450  ballotfilem2  13149  infpn2  13224  2strstr1g  13352  coseq00topi  15717  pigt3  15726