Theorem breqi 3851

Description: Equality inference for binary relations. (Contributed by NM, 19-Feb-2005.)

Hypothesis

Ref	Expression
breqi.1	|- R = S

Assertion

Ref	Expression
breqi	|- ( A R B <-> A S B )

Proof of Theorem breqi

Step	Hyp	Ref	Expression
1		breqi.1	. 2 |- R = S
2		breq 3847	. 2 |- ( R = S -> ( A R B <-> A S B ) )
3	1, 2	ax-mp 7	1 |- ( A R B <-> A S B )

Syntax hints:   <-> wb 103   = wceq 1289   class class class wbr 3845

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-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-clel 2084  df-br 3846

This theorem is referenced by:  f1ompt  5450  brtpos2  6016  tfrexlem  6099  brdifun  6319  ltpiord  6878  ltxrlt  7552  ltxr  9246