ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  breqtrri GIF version

Theorem breqtrri 3816
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtrr.1 𝐴𝑅𝐵
breqtrr.2 𝐶 = 𝐵
Assertion
Ref Expression
breqtrri 𝐴𝑅𝐶

Proof of Theorem breqtrri
StepHypRef Expression
1 breqtrr.1 . 2 𝐴𝑅𝐵
2 breqtrr.2 . . 3 𝐶 = 𝐵
32eqcomi 2060 . 2 𝐵 = 𝐶
41, 3breqtri 3814 1 𝐴𝑅𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1259   class class class wbr 3791
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2949  df-sn 3408  df-pr 3409  df-op 3411  df-br 3792
This theorem is referenced by:  3brtr4i  3819  ensn1  6306  0lt1sr  6907  0le2  8079  2pos  8080  3pos  8083  4pos  8086  5pos  8089  6pos  8090  7pos  8091  8pos  8092  9pos  8093  1lt2  8151  2lt3  8152  3lt4  8154  4lt5  8157  5lt6  8161  6lt7  8166  7lt8  8172  8lt9  8179  nn0le2xi  8288  numltc  8451  declti  8463  sqge0i  9505  faclbnd2  9609  3dvdsdec  10175  n2dvdsm1  10224  n2dvds3  10226  ex-fl  10258
  Copyright terms: Public domain W3C validator