Theorem rimrhm

Description: A ring isomorphism is a homomorphism. Compare gimghm . (Contributed by AV, 22-Oct-2019) Remove hypotheses. (Revised by SN, 10-Jan-2025)

	Ref	Expression
Assertion	rimrhm	|- ( F e. ( R RingIso S ) -> F e. ( R RingHom S ) )

Proof

Step	Hyp	Ref	Expression
1		isrim0	|- ( F e. ( R RingIso S ) <-> ( F e. ( R RingHom S ) /\ `' F e. ( S RingHom R ) ) )
2	1	simplbi	|- ( F e. ( R RingIso S ) -> F e. ( R RingHom S ) )