Theorem ercl2

Description: Elementhood in the field of an equivalence relation. (Contributed by Mario Carneiro, 12-Aug-2015)

	Ref	Expression
Hypotheses	ersym.1	|- ( ph -> R Er X )
	ersym.2	|- ( ph -> A R B )
Assertion	ercl2	|- ( ph -> B e. X )

Proof

Step	Hyp	Ref	Expression
1		ersym.1	|- ( ph -> R Er X )
2		ersym.2	|- ( ph -> A R B )
3	1 2	ersym	|- ( ph -> B R A )
4	1 3	ercl	|- ( ph -> B e. X )