Theorem rhmf

Description: A ring homomorphism is a function. (Contributed by Stefan O'Rear, 8-Mar-2015)

	Ref	Expression
Hypotheses	rhmf.b	|- B = ( Base ` R )
	rhmf.c	|- C = ( Base ` S )
Assertion	rhmf	|- ( F e. ( R RingHom S ) -> F : B --> C )

Proof

Step	Hyp	Ref	Expression
1		rhmf.b	|- B = ( Base ` R )
2		rhmf.c	|- C = ( Base ` S )
3		rhmghm	|- ( F e. ( R RingHom S ) -> F e. ( R GrpHom S ) )
4	1 2	ghmf	|- ( F e. ( R GrpHom S ) -> F : B --> C )
5	3 4	syl	|- ( F e. ( R RingHom S ) -> F : B --> C )