Theorem breq2i 3813

Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.)

Hypothesis

Ref	Expression
breq1i.1	|- A = B

Assertion

Ref	Expression
breq2i	|- ( C R A <-> C R B )

Proof of Theorem breq2i

Step	Hyp	Ref	Expression
1		breq1i.1	. 2 |- A = B
2		breq2 3809	. 2 |- ( A = B -> ( C R A <-> C R B ) )
3	1, 2	ax-mp 7	1 |- ( C R A <-> C R B )

Syntax hints:   <-> wb 103   = wceq 1285   class class class wbr 3805

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-sn 3422  df-pr 3423  df-op 3425  df-br 3806

This theorem is referenced by:  breqtri  3828  en1  6367  snnen2og  6415  1nen2  6417  pm54.43  6570  caucvgprprlemval  6992  caucvgprprlemmu  6999  caucvgsr  7092  pitonnlem1  7127  lt0neg2  7692  le0neg2  7694  negap0  7848  recexaplem2  7861  recgt1  8094  crap0  8154  addltmul  8386  nn0lt10b  8561  nn0lt2  8562  3halfnz  8577  xlt0neg2  9034  xle0neg2  9036  iccshftr  9144  iccshftl  9146  iccdil  9148  icccntr  9150  fihashen1  9875  cjap0  9995  abs00ap  10149  3dvdsdec  10472  3dvds2dec  10473  ndvdsi  10540  3prm  10717  prmfac1  10738