Theorem 3brtr4i 4075

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 4066	. 2 |- C R B
4		3brtr4.3	. 2 |- D = B
5	3, 4	breqtrri 4072	1 |- C R D

Syntax hints:   = wceq 1373   class class class wbr 4045

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642  df-br 4046

This theorem is referenced by:  1lt2nq  7521  0lt1sr  7880  ax0lt1  7991  declt  9533  decltc  9534  decle  9539  frecfzennn  10573  fsumabs  11809  basendxltplusgndx  12978  2strbasg  12985  2stropg  12986  basendxlttsetndx  13055  basendxltplendx  13069  basendxltdsndx  13084  basendxltunifndx  13094  basendxltedgfndx  15642