Theorem breqi 3344

Description: Equality inference for binary relations.

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 3340	. 2 |- (R = S -> (ARB <-> ASB))
3	1, 2	ax-mp 7	1 |- (ARB <-> ASB)

Syntax hints:   <-> wb 163   = wceq 1298   class class class wbr 3338

This theorem is referenced by:  brabsb 3566  avril1 10142  axhcompl 10500  hhcmpl 10702  brtxp 14067  fneerdm 15498  topfneec 15501  pltval 16781

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-17 1317  ax-4 1319  ax-5o 1321  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-cleq 1877  df-clel 1880  df-br 3339

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