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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 e. A -> [ B ] ( `' _E \|` A ) = B )

Proof

Step	Hyp	Ref	Expression
1		elecreseq	\|- ( 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 )