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Metamath Proof Explorer

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	$⊢ B \in A \to [B] ({E^{-1} ↾}_{A}) = B$

Proof

Step	Hyp	Ref	Expression
1		elecreseq	$⊢ B \in A \to [B] ({E^{-1} ↾}_{A}) = [B] E^{-1}$
2		eccnvep	$⊢ B \in A \to [B] E^{-1} = B$
3	1 2	eqtrd	$⊢ B \in A \to [B] ({E^{-1} ↾}_{A}) = B$