Theorem ertr4d

Description: A transitivity relation for equivalences. (Contributed by Mario Carneiro, 9-Jul-2014)

	Ref	Expression
Hypotheses	ersymb.1	|- ( ph -> R Er X )
	ertr4d.5	|- ( ph -> A R B )
	ertr4d.6	|- ( ph -> C R B )
Assertion	ertr4d	|- ( ph -> A R C )

Proof

Step	Hyp	Ref	Expression
1		ersymb.1	|- ( ph -> R Er X )
2		ertr4d.5	|- ( ph -> A R B )
3		ertr4d.6	|- ( ph -> C R B )
4	1 3	ersym	|- ( ph -> B R C )
5	1 2 4	ertrd	|- ( ph -> A R C )