Theorem eqvreltr4d

Description: A transitivity relation for equivalences. (Contributed by Mario Carneiro, 9-Jul-2014) (Revised by Peter Mazsa, 2-Jun-2019)

	Ref	Expression
Hypotheses	eqvreltr4d.1	|- ( ph -> EqvRel R )
	eqvreltr4d.2	|- ( ph -> A R B )
	eqvreltr4d.3	|- ( ph -> C R B )
Assertion	eqvreltr4d	|- ( ph -> A R C )

Proof

Step	Hyp	Ref	Expression
1		eqvreltr4d.1	|- ( ph -> EqvRel R )
2		eqvreltr4d.2	|- ( ph -> A R B )
3		eqvreltr4d.3	|- ( ph -> C R B )
4	1 3	eqvrelsym	|- ( ph -> B R C )
5	1 2 4	eqvreltrd	|- ( ph -> A R C )