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Theorem 3brtr4i 3879
 Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr4.1 𝐴𝑅𝐵
3brtr4.2 𝐶 = 𝐴
3brtr4.3 𝐷 = 𝐵
Assertion
Ref Expression
3brtr4i 𝐶𝑅𝐷

Proof of Theorem 3brtr4i
StepHypRef Expression
1 3brtr4.2 . . 3 𝐶 = 𝐴
2 3brtr4.1 . . 3 𝐴𝑅𝐵
31, 2eqbrtri 3870 . 2 𝐶𝑅𝐵
4 3brtr4.3 . 2 𝐷 = 𝐵
53, 4breqtrri 3876 1 𝐶𝑅𝐷
 Colors of variables: wff set class Syntax hints:   = wceq 1290   class class class wbr 3851 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-un 3004  df-sn 3456  df-pr 3457  df-op 3459  df-br 3852 This theorem is referenced by:  1lt2nq  7026  0lt1sr  7372  ax0lt1  7472  declt  8965  decltc  8966  decle  8971  frecfzennn  9894  fsumabs  10920  2strbasg  11656  2stropg  11657
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