Step | Hyp | Ref
| Expression |
1 | | cgzu 34107 |
. 2
class
AxUn |
2 | | c2o 8410 |
. . . . . . . 8
class
2o |
3 | | c1o 8409 |
. . . . . . . 8
class
1o |
4 | | cgoe 33991 |
. . . . . . . 8
class
∈𝑔 |
5 | 2, 3, 4 | co 7361 |
. . . . . . 7
class
(2o∈𝑔1o) |
6 | | c0 4286 |
. . . . . . . 8
class
∅ |
7 | 3, 6, 4 | co 7361 |
. . . . . . 7
class
(1o∈𝑔∅) |
8 | | cgoa 34091 |
. . . . . . 7
class
∧𝑔 |
9 | 5, 7, 8 | co 7361 |
. . . . . 6
class
((2o∈𝑔1o)∧𝑔(1o∈𝑔∅)) |
10 | 9, 3 | cgox 34096 |
. . . . 5
class
∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅)) |
11 | | cgoi 34092 |
. . . . 5
class
→𝑔 |
12 | 10, 5, 11 | co 7361 |
. . . 4
class
(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
13 | 12, 2 | cgol 33993 |
. . 3
class
∀𝑔2o(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
14 | 13, 3 | cgox 34096 |
. 2
class
∃𝑔1o∀𝑔2o(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
15 | 1, 14 | wceq 1542 |
1
wff AxUn =
∃𝑔1o∀𝑔2o(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |