Theorem breqi 3988

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 3984	. 2 |- ( R = S -> ( A R B <-> A S B ) )
3	1, 2	ax-mp 5	1 |- ( A R B <-> A S B )

Syntax hints:   <-> wb 104   = wceq 1343   class class class wbr 3982

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-ial 1522  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-clel 2161  df-br 3983

This theorem is referenced by:  f1ompt  5636  brtpos2  6219  tfrexlem  6302  brdifun  6528  ltpiord  7260  ltxrlt  7964  ltxr  9711  xmeterval  13075