Theorem 3brtr3i 4062

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

Hypotheses

Ref	Expression
3brtr3.1	|- A R B
3brtr3.2	|- A = C
3brtr3.3	|- B = D

Assertion

Ref	Expression
3brtr3i	|- C R D

Proof of Theorem 3brtr3i

Step	Hyp	Ref	Expression
1		3brtr3.2	. . 3 |- A = C
2		3brtr3.1	. . 3 |- A R B
3	1, 2	eqbrtrri 4056	. 2 |- C R B
4		3brtr3.3	. 2 |- B = D
5	3, 4	breqtri 4058	1 |- C R D

Syntax hints:   = wceq 1364   class class class wbr 4033

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629  df-op 3631  df-br 4034

This theorem is referenced by:  suplocsrlempr  7874  iap0  9214  ef01bndlem  11921