Theorem 3brtr4i 4683

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

Hypotheses

Ref	Expression
3brtr4.1	|- A R B
3brtr4.2	|- C = A
3brtr4.3	|- D = B

Assertion

Ref	Expression
3brtr4i	|- C R D

Proof of Theorem 3brtr4i

Step	Hyp	Ref	Expression
1		3brtr4.2	. . 3 |- C = A
2		3brtr4.1	. . 3 |- A R B
3	1, 2	eqbrtri 4674	. 2 |- C R B
4		3brtr4.3	. 2 |- D = B
5	3, 4	breqtrri 4680	1 |- C R D

Syntax hints:   = wceq 1483   class class class wbr 4653

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-br 4654

This theorem is referenced by:  1lt2nq  9795  0lt1sr  9916  declt  11530  decltOLD  11531  decltc  11532  decltcOLD  11533  decle  11540  decleOLD  11543  fzennn  12767  faclbnd4lem1  13080  fsumabs  14533  ovolfiniun  23269  log2ublem3  24675  log2ub  24676  emgt0  24733  bclbnd  25005  bposlem8  25016  baseltedgf  25872  nmblolbii  27654  normlem6  27972  norm-ii-i  27994  nmbdoplbi  28883  dp2lt  29592  dp2ltsuc  29593  dp2ltc  29594  dplt  29612  dpltc  29615  dpmul4  29622  hgt750lemd  30726  hgt750lem  30729  supxrltinfxr  39677  nnsum4primesevenALTV  41689