Detailed syntax breakdown of Definition df-gzinf
Step | Hyp | Ref
| Expression |
1 | | cgzi 33400 |
. 2
class
AxInf |
2 | | c0 4258 |
. . . . 5
class
∅ |
3 | | c1o 8279 |
. . . . 5
class
1o |
4 | | cgoe 33282 |
. . . . 5
class
∈𝑔 |
5 | 2, 3, 4 | co 7269 |
. . . 4
class
(∅∈𝑔1o) |
6 | | c2o 8280 |
. . . . . . 7
class
2o |
7 | 6, 3, 4 | co 7269 |
. . . . . 6
class
(2o∈𝑔1o) |
8 | 6, 2, 4 | co 7269 |
. . . . . . . 8
class
(2o∈𝑔∅) |
9 | | cgoa 33382 |
. . . . . . . 8
class
∧𝑔 |
10 | 8, 5, 9 | co 7269 |
. . . . . . 7
class
((2o∈𝑔∅)∧𝑔(∅∈𝑔1o)) |
11 | 10, 2 | cgox 33387 |
. . . . . 6
class
∃𝑔∅((2o∈𝑔∅)∧𝑔(∅∈𝑔1o)) |
12 | | cgoi 33383 |
. . . . . 6
class
→𝑔 |
13 | 7, 11, 12 | co 7269 |
. . . . 5
class
((2o∈𝑔1o)
→𝑔
∃𝑔∅((2o∈𝑔∅)∧𝑔(∅∈𝑔1o))) |
14 | 13, 6 | cgol 33284 |
. . . 4
class
∀𝑔2o((2o∈𝑔1o)
→𝑔
∃𝑔∅((2o∈𝑔∅)∧𝑔(∅∈𝑔1o))) |
15 | 5, 14, 9 | co 7269 |
. . 3
class
((∅∈𝑔1o)∧𝑔∀𝑔2o((2o∈𝑔1o)
→𝑔
∃𝑔∅((2o∈𝑔∅)∧𝑔(∅∈𝑔1o)))) |
16 | 15, 3 | cgox 33387 |
. 2
class
∃𝑔1o((∅∈𝑔1o)∧𝑔∀𝑔2o((2o∈𝑔1o)
→𝑔 ∃𝑔∅((2o∈𝑔∅)∧𝑔(∅∈𝑔1o)))) |
17 | 1, 16 | wceq 1539 |
1
wff AxInf =
∃𝑔1o((∅∈𝑔1o)∧𝑔∀𝑔2o((2o∈𝑔1o)
→𝑔 ∃𝑔∅((2o∈𝑔∅)∧𝑔(∅∈𝑔1o)))) |