Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|- (/) = (/) |
2 |
|
f1o00 |
|- ( f : (/) -1-1-onto-> (/) <-> ( f = (/) /\ (/) = (/) ) ) |
3 |
1 2
|
mpbiran2 |
|- ( f : (/) -1-1-onto-> (/) <-> f = (/) ) |
4 |
3
|
abbii |
|- { f | f : (/) -1-1-onto-> (/) } = { f | f = (/) } |
5 |
|
eqid |
|- ( SymGrp ` (/) ) = ( SymGrp ` (/) ) |
6 |
|
eqid |
|- ( Base ` ( SymGrp ` (/) ) ) = ( Base ` ( SymGrp ` (/) ) ) |
7 |
5 6
|
symgbas |
|- ( Base ` ( SymGrp ` (/) ) ) = { f | f : (/) -1-1-onto-> (/) } |
8 |
|
df-sn |
|- { (/) } = { f | f = (/) } |
9 |
4 7 8
|
3eqtr4i |
|- ( Base ` ( SymGrp ` (/) ) ) = { (/) } |