Theorem breqi 4009

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 4005	. 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 105   = wceq 1353   class class class wbr 4003

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173  df-br 4004

This theorem is referenced by:  f1ompt  5667  brtpos2  6251  tfrexlem  6334  brdifun  6561  ltpiord  7317  ltxrlt  8021  ltxr  9773  xmeterval  13828