Theorem rnghmf

Description: A ring homomorphism is a function. (Contributed by AV, 23-Feb-2020)

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

Proof

Step	Hyp	Ref	Expression
1		rnghmf.b	|- B = ( Base ` R )
2		rnghmf.c	|- C = ( Base ` S )
3		rnghmghm	|- ( F e. ( R RngHom 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 RngHom S ) -> F : B --> C )