Theorem eccnvepres2

Description: The restricted converse epsilon coset of an element of the restriction is the element itself. (Contributed by Peter Mazsa, 16-Jul-2019)

	Ref	Expression
Assertion	eccnvepres2	|- ( B e. A -> [ B ] ( `' _E |` A ) = B )

Proof

Step	Hyp	Ref	Expression
1		ecres2	|- ( B e. A -> [ B ] ( `' _E |` A ) = [ B ] `' _E )
2		eccnvep	|- ( B e. A -> [ B ] `' _E = B )
3	1 2	eqtrd	|- ( B e. A -> [ B ] ( `' _E |` A ) = B )