Theorem lmimlmhm

Description: An isomorphism of modules is a homomorphism. (Contributed by Stefan O'Rear, 21-Jan-2015)

	Ref	Expression
Assertion	lmimlmhm	|- ( F e. ( R LMIso S ) -> F e. ( R LMHom S ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	|- ( Base ` R ) = ( Base ` R )
2		eqid	|- ( Base ` S ) = ( Base ` S )
3	1 2	islmim	|- ( F e. ( R LMIso S ) <-> ( F e. ( R LMHom S ) /\ F : ( Base ` R ) -1-1-onto-> ( Base ` S ) ) )
4	3	simplbi	|- ( F e. ( R LMIso S ) -> F e. ( R LMHom S ) )