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 ) ) |
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 ) ) |