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	$$⊢B\in A\to \left[B\right]\left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)=B$$

Proof

Step	Hyp	Ref	Expression
1		ecres2	$$⊢B\in A\to \left[B\right]\left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)=\left[B\right]{\mathrm{E}}^{-1}$$
2		eccnvep	$$⊢B\in A\to \left[B\right]{\mathrm{E}}^{-1}=B$$
3	1 2	eqtrd	$$⊢B\in A\to \left[B\right]\left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)=B$$