Theorem 3brtr4i 4114

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 4105	. 2 |- C R B
4		3brtr4.3	. 2 |- D = B
5	3, 4	breqtrri 4111	1 |- C R D

Syntax hints:   = wceq 1395   class class class wbr 4084

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2802  df-un 3202  df-sn 3673  df-pr 3674  df-op 3676  df-br 4085

This theorem is referenced by:  1lt2nq  7614  0lt1sr  7973  ax0lt1  8084  declt  9626  decltc  9627  decle  9632  frecfzennn  10676  fsumabs  12013  basendxltplusgndx  13183  2strbasg  13190  2stropg  13191  basendxlttsetndx  13260  basendxltplendx  13274  basendxltdsndx  13289  basendxltunifndx  13299  basendxltedgfndx  15848