Theorem breqi 2620

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 2616	. 2 |- (R = S -> (ARB <-> ASB))
3	1, 2	ax-mp 7	1 |- (ARB <-> ASB)

Syntax hints:   <-> wb 146   = wceq 954   class class class wbr 2614

This theorem is referenced by:  brabsb 2811  avril1 8723  axhcompl 8807  hhcmpl 9008

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-17 969  ax-4 971  ax-5o 973  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-cleq 1467  df-clel 1470  df-br 2615

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