Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl5eqbr Unicode version

Theorem syl5eqbr 3797
 Description: B chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999.)
Hypotheses
Ref Expression
syl5eqbr.1
syl5eqbr.2
Assertion
Ref Expression
syl5eqbr

Proof of Theorem syl5eqbr
StepHypRef Expression
1 syl5eqbr.2 . 2
2 syl5eqbr.1 . 2
3 eqid 2040 . 2
41, 2, 33brtr4g 3796 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   class class class wbr 3764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765 This theorem is referenced by:  xp1en  6297  caucvgprlemm  6766  intqfrac2  9161  bernneq2  9370
 Copyright terms: Public domain W3C validator