Theorem 3brtr4i 4118

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 4109	. 2 |- C R B
4		3brtr4.3	. 2 |- D = B
5	3, 4	breqtrri 4115	1 |- C R D

Syntax hints:   = wceq 1397   class class class wbr 4088

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676  df-op 3678  df-br 4089

This theorem is referenced by:  1lt2nq  7625  0lt1sr  7984  ax0lt1  8095  declt  9637  decltc  9638  decle  9643  frecfzennn  10687  fsumabs  12025  basendxltplusgndx  13195  2strbasg  13202  2stropg  13203  basendxlttsetndx  13272  basendxltplendx  13286  basendxltdsndx  13301  basendxltunifndx  13311  basendxltedgfndx  15860