Theorem breqi 4645

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

Hypothesis

Ref	Expression
breqi.1	|- R = S

Assertion

Ref	Expression
breqi	|- (ARB <-> ASB)

Proof of Theorem breqi

Step	Hyp	Ref	Expression
1		breqi.1	. 2 |- R = S
2		breq 4641	. 2 |- (R = S -> (ARB <-> ASB))
3	1, 2	ax-mp 8	1 |- (ARB <-> ASB)

Syntax hints:   <-> wb 176   = wceq 1642   class class class wbr 4639

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349  df-br 4640

This theorem is referenced by:  brres  4949  trtxp  5781  brtxp  5783  brimage  5793  qrpprod  5836  brpprod  5839  fnfullfunlem1  5856  ersymtr  5932  porta  5933  sopc  5934  weds  5938  brltc  6114  nchoicelem8  6296  nchoicelem19  6307