Theorem trcleq1

Description: Equality of relations implies equality of transitive closures. (Contributed by RP, 9-May-2020)

	Ref	Expression
Assertion	trcleq1	|- ( R = S -> |^| { r | ( R C_ r /\ ( r o. r ) C_ r ) } = |^| { r | ( S C_ r /\ ( r o. r ) C_ r ) } )

Proof

Step	Hyp	Ref	Expression
1		cleq1	|- ( R = S -> |^| { r | ( R C_ r /\ ( r o. r ) C_ r ) } = |^| { r | ( S C_ r /\ ( r o. r ) C_ r ) } )