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Metamath Proof Explorer

Theorem rimrcl2

Description: Reverse closure of a ring isomorphism. (Contributed by SN, 19-Feb-2025)

		Ref	Expression
	Assertion	rimrcl2	$⊢ F \in (R RingIso S) \to S \in Ring$

Step	Hyp	Ref	Expression
1		rimrhm	$⊢ F \in (R RingIso S) \to F \in (R RingHom S)$
2		rhmrcl2	$⊢ F \in (R RingHom S) \to S \in Ring$
3	1 2	syl	$⊢ F \in (R RingIso S) \to S \in Ring$