| Step | Hyp | Ref
| Expression |
|---|
| 1 | | ssdif0 4356 |
. . . . 5
β’ (π β π β (π β π) = β
) |
| 2 | | eqss 3990 |
. . . . . . . . 9
β’ (π = π β (π β π β§ π β π)) |
| 3 | | fveq2 6882 |
. . . . . . . . . . . . 13
β’ (π = π β ((intβπ½)βπ) = ((intβπ½)βπ)) |
| 4 | | clscld.1 |
. . . . . . . . . . . . . 14
β’ π = βͺ
π½ |
| 5 | 4 | ntrtop 22898 |
. . . . . . . . . . . . 13
β’ (π½ β Top β
((intβπ½)βπ) = π) |
| 6 | 3, 5 | sylan9eqr 2786 |
. . . . . . . . . . . 12
β’ ((π½ β Top β§ π = π) β ((intβπ½)βπ) = π) |
| 7 | 6 | eqeq1d 2726 |
. . . . . . . . . . 11
β’ ((π½ β Top β§ π = π) β (((intβπ½)βπ) = β
β π = β
)) |
| 8 | 7 | biimpd 228 |
. . . . . . . . . 10
β’ ((π½ β Top β§ π = π) β (((intβπ½)βπ) = β
β π = β
)) |
| 9 | 8 | ex 412 |
. . . . . . . . 9
β’ (π½ β Top β (π = π β (((intβπ½)βπ) = β
β π = β
))) |
| 10 | 2, 9 | biimtrrid 242 |
. . . . . . . 8
β’ (π½ β Top β ((π β π β§ π β π) β (((intβπ½)βπ) = β
β π = β
))) |
| 11 | 10 | expd 415 |
. . . . . . 7
β’ (π½ β Top β (π β π β (π β π β (((intβπ½)βπ) = β
β π = β
)))) |
| 12 | 11 | com34 91 |
. . . . . 6
β’ (π½ β Top β (π β π β (((intβπ½)βπ) = β
β (π β π β π = β
)))) |
| 13 | 12 | imp32 418 |
. . . . 5
β’ ((π½ β Top β§ (π β π β§ ((intβπ½)βπ) = β
)) β (π β π β π = β
)) |
| 14 | 1, 13 | biimtrrid 242 |
. . . 4
β’ ((π½ β Top β§ (π β π β§ ((intβπ½)βπ) = β
)) β ((π β π) = β
β π = β
)) |
| 15 | 14 | necon3d 2953 |
. . 3
β’ ((π½ β Top β§ (π β π β§ ((intβπ½)βπ) = β
)) β (π β β
β (π β π) β β
)) |
| 16 | 15 | imp 406 |
. 2
β’ (((π½ β Top β§ (π β π β§ ((intβπ½)βπ) = β
)) β§ π β β
) β (π β π) β β
) |
| 17 | 16 | an32s 649 |
1
β’ (((π½ β Top β§ π β β
) β§ (π β π β§ ((intβπ½)βπ) = β
)) β (π β π) β β
) |
