Step | Hyp | Ref
| Expression |
1 | | coppcc 36115 |
. 2
class
-āĢ
|
2 | | vx |
. . 3
setvar š„ |
3 | | cccbar 36091 |
. . . 4
class
āĢ
|
4 | | ccchat 36108 |
. . . 4
class
āĢ |
5 | 3, 4 | cun 3946 |
. . 3
class
(āĢ
āŖ āĢ) |
6 | 2 | cv 1540 |
. . . . 5
class š„ |
7 | | cinfty 36106 |
. . . . 5
class
ā |
8 | 6, 7 | wceq 1541 |
. . . 4
wff š„ = ā |
9 | | cc 11107 |
. . . . . 6
class
ā |
10 | 6, 9 | wcel 2106 |
. . . . 5
wff š„ ā ā |
11 | | vy |
. . . . . . . . 9
setvar š¦ |
12 | 11 | cv 1540 |
. . . . . . . 8
class š¦ |
13 | | caddcc 36113 |
. . . . . . . 8
class
+āĢ
|
14 | 6, 12, 13 | co 7408 |
. . . . . . 7
class (š„ +āĢ
š¦) |
15 | | cc0 11109 |
. . . . . . 7
class
0 |
16 | 14, 15 | wceq 1541 |
. . . . . 6
wff (š„ +āĢ
š¦) = 0 |
17 | 16, 11, 9 | crio 7363 |
. . . . 5
class
(ā©š¦
ā ā (š„
+āĢ
š¦) = 0) |
18 | | chalf 36079 |
. . . . . . . 8
class
1/2 |
19 | | c0r 10860 |
. . . . . . . 8
class
0R |
20 | 18, 19 | cop 4634 |
. . . . . . 7
class
āØ1/2, 0Rā© |
21 | 6, 20, 13 | co 7408 |
. . . . . 6
class (š„ +āĢ
āØ1/2, 0Rā©) |
22 | | cinftyexpitau 36074 |
. . . . . 6
class
+āeiĻ |
23 | 21, 22 | cfv 6543 |
. . . . 5
class
(+āeiĻā(š„ +āĢ
āØ1/2,
0Rā©)) |
24 | 10, 17, 23 | cif 4528 |
. . . 4
class if(š„ ā ā,
(ā©š¦ ā
ā (š„
+āĢ
š¦) = 0),
(+āeiĻā(š„ +āĢ
āØ1/2,
0Rā©))) |
25 | 8, 7, 24 | cif 4528 |
. . 3
class if(š„ = ā, ā, if(š„ ā ā,
(ā©š¦ ā
ā (š„
+āĢ
š¦) = 0),
(+āeiĻā(š„ +āĢ
āØ1/2,
0Rā©)))) |
26 | 2, 5, 25 | cmpt 5231 |
. 2
class (š„ ā (āĢ
āŖ
āĢ) ā¦ if(š„ = ā, ā, if(š„ ā ā, (ā©š¦ ā ā (š„ +āĢ
š¦) = 0),
(+āeiĻā(š„ +āĢ
āØ1/2,
0Rā©))))) |
27 | 1, 26 | wceq 1541 |
1
wff
-āĢ
= (š„ ā (āĢ
āŖ āĢ)
ā¦ if(š„ = ā,
ā, if(š„ ā
ā, (ā©š¦
ā ā (š„
+āĢ
š¦) = 0),
(+āeiĻā(š„ +āĢ
āØ1/2,
0Rā©))))) |