Description: A homomorphism of left modules has a left module as domain. (Contributed by Stefan O'Rear, 1-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | lmhmlmod1 | |- ( F e. ( S LMHom T ) -> S e. LMod ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- ( Scalar ` S ) = ( Scalar ` S ) |
|
2 | eqid | |- ( Scalar ` T ) = ( Scalar ` T ) |
|
3 | 1 2 | lmhmlem | |- ( F e. ( S LMHom T ) -> ( ( S e. LMod /\ T e. LMod ) /\ ( F e. ( S GrpHom T ) /\ ( Scalar ` T ) = ( Scalar ` S ) ) ) ) |
4 | 3 | simplld | |- ( F e. ( S LMHom T ) -> S e. LMod ) |