Description: An isomorphism of left modules is a bijection. (Contributed by Stefan O'Rear, 21-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | islmim.b | |- B = ( Base ` R ) |
|
islmim.c | |- C = ( Base ` S ) |
||
Assertion | lmimf1o | |- ( F e. ( R LMIso S ) -> F : B -1-1-onto-> C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | islmim.b | |- B = ( Base ` R ) |
|
2 | islmim.c | |- C = ( Base ` S ) |
|
3 | 1 2 | islmim | |- ( F e. ( R LMIso S ) <-> ( F e. ( R LMHom S ) /\ F : B -1-1-onto-> C ) ) |
4 | 3 | simprbi | |- ( F e. ( R LMIso S ) -> F : B -1-1-onto-> C ) |