Theorem.
(st),
(sv),
(pr),
(sv),
(sv),
(
,
), (
,
), (
,
), (
,
), (
,
), (
,
),
( bound in ) |
([ / ]![]() ![]() ![]() ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))) |
| Hyp | Ref | Line | Expr |
| Hypo | 1 | ( bound in ) | |
| df-sb | 2 | ([ / ]![]() ![]() ![]() ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))) | |
| eqt> | 3 | ((![]() ![]() ) ((![]() ![]() ) (![]() ![]() ))) | |
| 3 | bi.bldan<d | 4 | ((![]() ![]() ) (((![]() ![]() )![]() ) ((![]() ![]() )![]() ))) |
| ax17-bv | 5 | ( bound in (![]() ![]() )) | |
| 4, 5 | bi.bldexd | 6 | ((![]() ![]() ) (![]() ((![]() ![]() )![]() )![]() ![]() ((![]() ![]() )![]() ))) |
| eqt< | 7 | ((![]() ![]() ) ((![]() ![]() ) (![]() ![]() ))) | |
| 6, 7 | bi.bldan<>d | 8 | ((![]() ![]() ) (((![]() ![]() )![]() ![]() ((![]() ![]() )![]() )) ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() )))) |
| ax17-bv | 9 | ( bound in ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))) | |
| ax17-bv | 10 | ( bound in (![]() ![]() )) | |
| ax17-bv | 11 | ( bound in (![]() ![]() )) | |
| 1, 11 | bv-∧ | 12 | ( bound in ((![]() ![]() )![]() )) |
| 12 | bv-∃ | 13 | ( bound in ![]() ((![]() ![]() )![]() )) |
| 10, 13 | bv-∧ | 14 | ( bound in ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))) |
| 8, 9, 14 | cbvex | 15 | (![]() ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))![]() ![]() ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))) |
| 2, 15 | bitr | 16 | ([ / ]![]() ![]() ![]() ((![]() ![]() )![]() ![]() ((![]() ![]() )![]() ))) |