Theorem.
(sv),
(sv),
(pr),
(pr),
((![]() ![]() ) (![]() ![]() )) |
( bound in ) |
( bound in ) |
(![]() ![]() ![]() ![]() ![]() ![]() ) |
| Hyp | Ref | Line | Expr |
| Hypo | 1 | ((![]() ![]() ) (![]() ![]() )) | |
| 2 | ( bound in ) | ||
| 3 | ( bound in ) | ||
| 3 | df-Bvp | 4 | (![]() ![]() ![]() ![]() ) |
| 4 | syl< | 5 | ((![]() ![]() ) (![]() ![]() ![]() ![]() )) |
| 2 | df-Bvp | 6 | (![]() ![]() ![]() ![]() ) |
| 6 | ax1 | 7 | ((![]() ![]() ) (![]() ![]() ![]() ![]() )) |
| 1 | ax1 | 8 | ((![]() ![]() ) ((![]() ![]() ) (![]() ![]() ))) |
| 5, 7, 8 | cbv1 | 9 | (![]() ![]() ![]() (![]() ![]() ) (![]() ![]() ![]() ![]() ![]() ![]() )) |
| id | 10 | (![]() ![]() ) | |
| 10 | ax-gen | 11 | ![]() (![]() ![]() ) |
| 11 | ax-gen | 12 | ![]() ![]() ![]() (![]() ![]() ) |
| 9, 12 | ax-mp | 13 | (![]() ![]() ![]() ![]() ![]() ![]() ) |