Step | Hyp | Ref
| Expression |
1 | | cgze 34104 |
. 2
class
AxExt |
2 | | c2o 8410 |
. . . . . 6
class
2o |
3 | | c0 4286 |
. . . . . 6
class
∅ |
4 | | cgoe 33991 |
. . . . . 6
class
∈𝑔 |
5 | 2, 3, 4 | co 7361 |
. . . . 5
class
(2o∈𝑔∅) |
6 | | c1o 8409 |
. . . . . 6
class
1o |
7 | 2, 6, 4 | co 7361 |
. . . . 5
class
(2o∈𝑔1o) |
8 | | cgob 34094 |
. . . . 5
class
↔𝑔 |
9 | 5, 7, 8 | co 7361 |
. . . 4
class
((2o∈𝑔∅)
↔𝑔
(2o∈𝑔1o)) |
10 | 9, 2 | cgol 33993 |
. . 3
class
∀𝑔2o((2o∈𝑔∅)
↔𝑔
(2o∈𝑔1o)) |
11 | | cgoq 34095 |
. . . 4
class
=𝑔 |
12 | 3, 6, 11 | co 7361 |
. . 3
class
(∅=𝑔1o) |
13 | | cgoi 34092 |
. . 3
class
→𝑔 |
14 | 10, 12, 13 | co 7361 |
. 2
class
(∀𝑔2o((2o∈𝑔∅)
↔𝑔 (2o∈𝑔1o))
→𝑔 (∅=𝑔1o)) |
15 | 1, 14 | wceq 1542 |
1
wff AxExt =
(∀𝑔2o((2o∈𝑔∅)
↔𝑔 (2o∈𝑔1o))
→𝑔 (∅=𝑔1o)) |