Theorem breqi 2630

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 2626	. 2 |- (R = S -> (ARB <-> ASB))
3	1, 2	ax-mp 7	1 |- (ARB <-> ASB)

Syntax hints:   <-> wb 146   = wceq 958   class class class wbr 2624

This theorem is referenced by:  brabsb 2822  avril1 8779  axhcompl 8863  hhcmpl 9064

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-cleq 1472  df-clel 1475  df-br 2625

Copyright terms: Public domain