Theorem 3brtr4i 4139

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 4130	. 2 |- C R B
4		3brtr4.3	. 2 |- D = B
5	3, 4	breqtrri 4136	1 |- C R D

Syntax hints:   = wceq 1398   class class class wbr 4109

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-v 2815  df-un 3215  df-sn 3695  df-pr 3696  df-op 3698  df-br 4110

This theorem is referenced by:  1lt2nq  7721  0lt1sr  8080  ax0lt1  8191  declt  9736  decltc  9737  decle  9742  frecfzennn  10788  fsumabs  12151  basendxltplusgndx  13326  2strbasg  13333  2stropg  13334  basendxlttsetndx  13403  basendxltplendx  13417  basendxltdsndx  13432  basendxltunifndx  13442  basendxltedgfndx  16005