Theorem 3brtr4i 4028

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 4019	. 2 |- C R B
4		3brtr4.3	. 2 |- D = B
5	3, 4	breqtrri 4025	1 |- C R D

Syntax hints:   = wceq 1353   class class class wbr 3998

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 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-un 3131  df-sn 3595  df-pr 3596  df-op 3598  df-br 3999

This theorem is referenced by:  1lt2nq  7380  0lt1sr  7739  ax0lt1  7850  declt  9384  decltc  9385  decle  9390  frecfzennn  10396  fsumabs  11441  2strbasg  12541  2stropg  12542  basendxlttsetndx  12595  basendxltdsndx  12612