Description: An isomorphism of rings is a bijection. (Contributed by AV, 22-Oct-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | rhmf1o.b | |- B = ( Base ` R ) |
|
rhmf1o.c | |- C = ( Base ` S ) |
||
Assertion | rimf1o | |- ( F e. ( R RingIso S ) -> F : B -1-1-onto-> C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rhmf1o.b | |- B = ( Base ` R ) |
|
2 | rhmf1o.c | |- C = ( Base ` S ) |
|
3 | 1 2 | isrim | |- ( F e. ( R RingIso S ) <-> ( F e. ( R RingHom S ) /\ F : B -1-1-onto-> C ) ) |
4 | 3 | simprbi | |- ( F e. ( R RingIso S ) -> F : B -1-1-onto-> C ) |