Description: Obsolete version of oppgtset as of 18-Oct-2024. Topology of an opposite group. (Contributed by Mario Carneiro, 17-Sep-2015) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | oppgbas.1 | |- O = ( oppG ` R ) |
|
| oppgtset.2 | |- J = ( TopSet ` R ) |
||
| Assertion | oppgtsetOLD | |- J = ( TopSet ` O ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | oppgbas.1 | |- O = ( oppG ` R ) |
|
| 2 | oppgtset.2 | |- J = ( TopSet ` R ) |
|
| 3 | df-tset | |- TopSet = Slot 9 |
|
| 4 | 9nn | |- 9 e. NN |
|
| 5 | 2re | |- 2 e. RR |
|
| 6 | 2lt9 | |- 2 < 9 |
|
| 7 | 5 6 | gtneii | |- 9 =/= 2 |
| 8 | 1 3 4 7 | oppglemOLD | |- ( TopSet ` R ) = ( TopSet ` O ) |
| 9 | 2 8 | eqtri | |- J = ( TopSet ` O ) |