Theorem 3brtr3i 4005

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)

Hypotheses

Ref	Expression
3brtr3.1	|- A R B
3brtr3.2	|- A = C
3brtr3.3	|- B = D

Assertion

Ref	Expression
3brtr3i	|- C R D

Proof of Theorem 3brtr3i

Step	Hyp	Ref	Expression
1		3brtr3.2	. . 3 |- A = C
2		3brtr3.1	. . 3 |- A R B
3	1, 2	eqbrtrri 3999	. 2 |- C R B
4		3brtr3.3	. 2 |- B = D
5	3, 4	breqtri 4001	1 |- C R D

Syntax hints:   = wceq 1342   class class class wbr 3976

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-3an 969  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2723  df-un 3115  df-sn 3576  df-pr 3577  df-op 3579  df-br 3977

This theorem is referenced by:  suplocsrlempr  7739  iap0  9071  ef01bndlem  11683