Theorem.
(pr),
(pr),
(pr),
((![]() (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) |
| Hyp | Ref | Line | Expr |
| bi> | 1 | ((![]() ![]() ) (![]() ![]() )) | |
| 1 | syl< | 2 | ((![]() (![]() ![]() )) (![]() (![]() ![]() ))) |
| 2 | ax2 | 3 | ((![]() (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) |
| bi< | 4 | ((![]() ![]() ) (![]() ![]() )) | |
| 4 | syl< | 5 | ((![]() (![]() ![]() )) (![]() (![]() ![]() ))) |
| 5 | ax2 | 6 | ((![]() (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) |
| 3, 6 | >bid | 7 | ((![]() (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) |
| bi> | 8 | (((![]() ![]() ) (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) | |
| 8 | ax2-converse | 9 | (((![]() ![]() ) (![]() ![]() )) (![]() (![]() ![]() ))) |
| bi< | 10 | (((![]() ![]() ) (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) | |
| 10 | ax2-converse | 11 | (((![]() ![]() ) (![]() ![]() )) (![]() (![]() ![]() ))) |
| 9, 11 | im.bldan<>d | 12 | (((![]() ![]() ) (![]() ![]() )) ((![]() ![]() ) ((![]() ![]() ) (![]() ![]() )))) |
| anidm | 13 | ((![]() ![]() )![]() ) | |
| 13 | bicomi | 14 | (![]() (![]() ![]() )) |
| dfbi | 15 | ((![]() ![]() ) ((![]() ![]() ) (![]() ![]() ))) | |
| 12, 14, 15 | <imtrg | 16 | (((![]() ![]() ) (![]() ![]() )) (![]() (![]() ![]() ))) |
| 7, 16 | >bii | 17 | ((![]() (![]() ![]() )) ((![]() ![]() ) (![]() ![]() ))) |