Theorem syl6breq 3824

Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999.)

Hypotheses

Ref	Expression
syl6breq.1	|- ( ph -> A R B )
syl6breq.2	|- B = C

Assertion

Ref	Expression
syl6breq	|- ( ph -> A R C )

Proof of Theorem syl6breq

Step	Hyp	Ref	Expression
1		syl6breq.1	. 2 |- ( ph -> A R B )
2		eqid 2081	. 2 |- A = A
3		syl6breq.2	. 2 |- B = C
4	1, 2, 3	3brtr3g 3816	1 |- ( ph -> A R C )

Syntax hints:   -> wi 4   = 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:  syl6breqr  3825  maxle2  10098