Theorem 3brtr3i 4464

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 4458	. 2 |- C R B
4		3brtr3.3	. 2 |- B = D
5	3, 4	breqtri 4460	1 |- C R D

Syntax hints:   = wceq 1383   class class class wbr 4437

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-br 4438

This theorem is referenced by:  supsrlem  9491  ef01bndlem  13901  pige3  22888  log2ublem1  23255  log2ub  23258  ppiublem1  23455  logfacrlim2  23479  chebbnd1  23635  nmoptri2i  26996  problem5  29001  fouriersw  31968