Theorem 3brtr3i 4474

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 4468	. 2 |- C R B
4		3brtr3.3	. 2 |- B = D
5	3, 4	breqtri 4470	1 |- C R D

Syntax hints:   = wceq 1379   class class class wbr 4447

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448

This theorem is referenced by:  supsrlem  9488  ef01bndlem  13780  pige3  22671  log2ublem1  23033  log2ub  23036  ppiublem1  23233  logfacrlim2  23257  chebbnd1  23413  nmoptri2i  26722  problem5  28526