Theorem 3brtr3g 4483

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 16-Jan-1997.)

Hypotheses

Ref	Expression
3brtr3g.1
3brtr3g.2
3brtr3g.3

Assertion

Ref	Expression
3brtr3g

Proof of Theorem 3brtr3g

Step	Hyp	Ref	Expression
1		3brtr3g.1	. 2
2		3brtr3g.2	. . 3
3		3brtr3g.3	. . 3
4	2, 3	breq12i 4461	. 2
5	1, 4	sylib 196	1

Syntax hints:  ->wi 4  =wceq 1395   class class class wbr 4452

This theorem is referenced by:  syl5eqbrr  4486  syl6breq  4491  ssenen  7711  adderpq  9355  mulerpq  9356  ltaddnq  9373  ege2le3  13825  ovolfiniun  21912  dvfsumlem3  22429  basellem9  23362  pnt2  23798  pnt  23799  siilem1  25766  omndaddr  27697  ogrpaddltrd  27710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453