Description: Obsolete version of oppgle as of 27-Oct-2024. less-than relation of an opposite group. (Contributed by Thierry Arnoux, 13-Apr-2018) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | oppglt.1 | |- O = ( oppG ` R ) |
|
| oppgle.2 | |- .<_ = ( le ` R ) |
||
| Assertion | oppgleOLD | |- .<_ = ( le ` O ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | oppglt.1 | |- O = ( oppG ` R ) |
|
| 2 | oppgle.2 | |- .<_ = ( le ` R ) |
|
| 3 | df-ple | |- le = Slot ; 1 0 |
|
| 4 | 10nn | |- ; 1 0 e. NN |
|
| 5 | 2re | |- 2 e. RR |
|
| 6 | 2lt10 | |- 2 < ; 1 0 |
|
| 7 | 5 6 | gtneii | |- ; 1 0 =/= 2 |
| 8 | 1 3 4 7 | oppglemOLD | |- ( le ` R ) = ( le ` O ) |
| 9 | 2 8 | eqtri | |- .<_ = ( le ` O ) |