Detailed syntax breakdown of Definition df-gzun
| Step | Hyp | Ref
| Expression |
|---|
| 1 | | cgzu 33311 |
. 2
class
AxUn |
| 2 | | c2o 8261 |
. . . . . . . 8
class
2o |
| 3 | | c1o 8260 |
. . . . . . . 8
class
1o |
| 4 | | cgoe 33195 |
. . . . . . . 8
class
∈𝑔 |
| 5 | 2, 3, 4 | co 7255 |
. . . . . . 7
class
(2o∈𝑔1o) |
| 6 | | c0 4253 |
. . . . . . . 8
class
∅ |
| 7 | 3, 6, 4 | co 7255 |
. . . . . . 7
class
(1o∈𝑔∅) |
| 8 | | cgoa 33295 |
. . . . . . 7
class
∧𝑔 |
| 9 | 5, 7, 8 | co 7255 |
. . . . . 6
class
((2o∈𝑔1o)∧𝑔(1o∈𝑔∅)) |
| 10 | 9, 3 | cgox 33300 |
. . . . 5
class
∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅)) |
| 11 | | cgoi 33296 |
. . . . 5
class
→𝑔 |
| 12 | 10, 5, 11 | co 7255 |
. . . 4
class
(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
| 13 | 12, 2 | cgol 33197 |
. . 3
class
∀𝑔2o(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
| 14 | 13, 3 | cgox 33300 |
. 2
class
∃𝑔1o∀𝑔2o(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
| 15 | 1, 14 | wceq 1539 |
1
wff AxUn =
∃𝑔1o∀𝑔2o(∃𝑔1o((2o∈𝑔1o)∧𝑔(1o∈𝑔∅))
→𝑔 (2o∈𝑔1o)) |
