Step | Hyp | Ref
| Expression |
1 | | cgzr 34105 |
. 2
class
AxRep |
2 | | vu |
. . 3
setvar π’ |
3 | | com 7806 |
. . . 4
class
Ο |
4 | | cfmla 33995 |
. . . 4
class
Fmla |
5 | 3, 4 | cfv 6500 |
. . 3
class
(FmlaβΟ) |
6 | 2 | cv 1541 |
. . . . . . . . 9
class π’ |
7 | | c1o 8409 |
. . . . . . . . 9
class
1o |
8 | 6, 7 | cgol 33993 |
. . . . . . . 8
class
βπ1oπ’ |
9 | | c2o 8410 |
. . . . . . . . 9
class
2o |
10 | | cgoq 34095 |
. . . . . . . . 9
class
=π |
11 | 9, 7, 10 | co 7361 |
. . . . . . . 8
class
(2o=π1o) |
12 | | cgoi 34092 |
. . . . . . . 8
class
βπ |
13 | 8, 11, 12 | co 7361 |
. . . . . . 7
class
(βπ1oπ’ βπ
(2o=π1o)) |
14 | 13, 9 | cgol 33993 |
. . . . . 6
class
βπ2o(βπ1oπ’ βπ
(2o=π1o)) |
15 | 14, 7 | cgox 34096 |
. . . . 5
class
βπ1oβπ2o(βπ1oπ’ βπ
(2o=π1o)) |
16 | | c3o 8411 |
. . . . 5
class
3o |
17 | 15, 16 | cgol 33993 |
. . . 4
class
βπ3oβπ1oβπ2o(βπ1oπ’ βπ (2o=π1o)) |
18 | | cgoe 33991 |
. . . . . . . 8
class
βπ |
19 | 9, 7, 18 | co 7361 |
. . . . . . 7
class
(2oβπ1o) |
20 | | c0 4286 |
. . . . . . . . . 10
class
β
|
21 | 16, 20, 18 | co 7361 |
. . . . . . . . 9
class
(3oβπβ
) |
22 | | cgoa 34091 |
. . . . . . . . 9
class
β§π |
23 | 21, 8, 22 | co 7361 |
. . . . . . . 8
class
((3oβπβ
)β§πβπ1oπ’) |
24 | 23, 16 | cgox 34096 |
. . . . . . 7
class
βπ3o((3oβπβ
)β§πβπ1oπ’) |
25 | | cgob 34094 |
. . . . . . 7
class
βπ |
26 | 19, 24, 25 | co 7361 |
. . . . . 6
class
((2oβπ1o)
βπ
βπ3o((3oβπβ
)β§πβπ1oπ’)) |
27 | 26, 9 | cgol 33993 |
. . . . 5
class
βπ2o((2oβπ1o)
βπ
βπ3o((3oβπβ
)β§πβπ1oπ’)) |
28 | 27, 7 | cgol 33993 |
. . . 4
class
βπ1oβπ2o((2oβπ1o)
βπ
βπ3o((3oβπβ
)β§πβπ1oπ’)) |
29 | 17, 28, 12 | co 7361 |
. . 3
class
(βπ3oβπ1oβπ2o(βπ1oπ’ βπ (2o=π1o)) βπ
βπ1oβπ2o((2oβπ1o) βπ
βπ3o((3oβπβ
)β§πβπ1oπ’))) |
30 | 2, 5, 29 | cmpt 5192 |
. 2
class (π’ β (FmlaβΟ)
β¦
(βπ3oβπ1oβπ2o(βπ1oπ’ βπ (2o=π1o)) βπ
βπ1oβπ2o((2oβπ1o) βπ
βπ3o((3oβπβ
)β§πβπ1oπ’)))) |
31 | 1, 30 | wceq 1542 |
1
wff AxRep =
(π’ β
(FmlaβΟ) β¦
(βπ3oβπ1oβπ2o(βπ1oπ’ βπ (2o=π1o)) βπ
βπ1oβπ2o((2oβπ1o) βπ
βπ3o((3oβπβ
)β§πβπ1oπ’)))) |