Theorem eccnvep

Description: The converse epsilon coset of a set is the set. (Contributed by Peter Mazsa, 27-Jan-2019)

	Ref	Expression
Assertion	eccnvep	$$⊢A\in V\to \left[A\right]{\mathrm{E}}^{-1}=A$$

Proof

Step	Hyp	Ref	Expression
1		eleccnvep	$$⊢A\in V\to \left(x\in \left[A\right]{\mathrm{E}}^{-1}\leftrightarrow x\in A\right)$$
2	1	eqrdv	$$⊢A\in V\to \left[A\right]{\mathrm{E}}^{-1}=A$$