Theorem breqi 2640

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 2636	. 2 ⊢ (R = S → (ARB ↔ ASB))
3	1, 2	ax-mp 7	1 ⊢ (ARB ↔ ASB)

Syntax hints:   ↔ wb 146   = wceq 960   class class class wbr 2634

This theorem is referenced by:  brabsb 2832  avril1 8808  axhcompl 8892  hhcmpl 9093

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 967  ax-17 975  ax-4 977  ax-5o 979  ax-ext 1464

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 985  df-cleq 1475  df-clel 1478  df-br 2635

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