Theorem breq2i 3793

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 3789	. 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 1284   class class class wbr 3785

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-br 3786

This theorem is referenced by:  breqtri  3808  en1  6302  snnen2og  6345  1nen2  6347  pm54.43  6459  caucvgprprlemval  6878  caucvgprprlemmu  6885  caucvgsr  6978  pitonnlem1  7013  lt0neg2  7573  le0neg2  7575  negap0  7729  recexaplem2  7742  recgt1  7975  crap0  8035  addltmul  8267  nn0lt10b  8428  nn0lt2  8429  3halfnz  8444  xlt0neg2  8906  xle0neg2  8908  iccshftr  9016  iccshftl  9018  iccdil  9020  icccntr  9022  cjap0  9794  abs00ap  9948  3dvdsdec  10264  3dvds2dec  10265  ndvdsi  10333  3prm  10510  prmfac1  10531