| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ssid |
|- { (/) } C_ { (/) } |
| 2 |
|
fvex |
|- ( EndoFMnd ` (/) ) e. _V |
| 3 |
|
p0ex |
|- { (/) } e. _V |
| 4 |
|
eqid |
|- ( SymGrp ` (/) ) = ( SymGrp ` (/) ) |
| 5 |
|
symgbas0 |
|- ( Base ` ( SymGrp ` (/) ) ) = { (/) } |
| 6 |
5
|
eqcomi |
|- { (/) } = ( Base ` ( SymGrp ` (/) ) ) |
| 7 |
|
eqid |
|- ( EndoFMnd ` (/) ) = ( EndoFMnd ` (/) ) |
| 8 |
4 6 7
|
symgressbas |
|- ( SymGrp ` (/) ) = ( ( EndoFMnd ` (/) ) |`s { (/) } ) |
| 9 |
|
efmndbas0 |
|- ( Base ` ( EndoFMnd ` (/) ) ) = { (/) } |
| 10 |
9
|
eqcomi |
|- { (/) } = ( Base ` ( EndoFMnd ` (/) ) ) |
| 11 |
8 10
|
ressid2 |
|- ( ( { (/) } C_ { (/) } /\ ( EndoFMnd ` (/) ) e. _V /\ { (/) } e. _V ) -> ( SymGrp ` (/) ) = ( EndoFMnd ` (/) ) ) |
| 12 |
1 2 3 11
|
mp3an |
|- ( SymGrp ` (/) ) = ( EndoFMnd ` (/) ) |
| 13 |
12
|
eqcomi |
|- ( EndoFMnd ` (/) ) = ( SymGrp ` (/) ) |