Theorem 3brtr4i 4480

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

Hypotheses

Ref	Expression
3brtr4.1
3brtr4.2
3brtr4.3

Assertion

Ref	Expression
3brtr4i

Proof of Theorem 3brtr4i

Step	Hyp	Ref	Expression
1		3brtr4.2	. . 3
2		3brtr4.1	. . 3
3	1, 2	eqbrtri 4471	. 2
4		3brtr4.3	. 2
5	3, 4	breqtrri 4477	1

Syntax hints:  =wceq 1395   class class class wbr 4452

This theorem is referenced by:  1lt2nq  9372  0lt1sr  9493  declt  11025  decltc  11026  fzennn  12078  faclbnd4lem1  12371  fsumabs  13615  ovolfiniun  21912  log2ublem3  23279  log2ub  23280  emgt0  23336  bclbnd  23555  bposlem8  23566  nmblolbii  25714  normlem6  26032  norm-ii-i  26054  nmbdoplbi  26943

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