Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  breq123d Unicode version

Theorem breq123d 3881
 Description: Equality deduction for a binary relation. (Contributed by NM, 29-Oct-2011.)
Hypotheses
Ref Expression
breq1d.1
breq123d.2
breq123d.3
Assertion
Ref Expression
breq123d

Proof of Theorem breq123d
StepHypRef Expression
1 breq1d.1 . . 3
2 breq123d.3 . . 3
31, 2breq12d 3880 . 2
4 breq123d.2 . . 3
54breqd 3878 . 2
63, 5bitrd 187 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1296   class class class wbr 3867 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 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-un 3017  df-sn 3472  df-pr 3473  df-op 3475  df-br 3868 This theorem is referenced by:  sbcbrg  3916  fmptco  5503
 Copyright terms: Public domain W3C validator