Detailed syntax breakdown of Definition df-gzext
| Step | Hyp | Ref
| Expression |
|---|
| 1 | | cgze 31343 |
. 2
class
AxExt |
| 2 | | c2o 7554 |
. . . . . 6
class
2𝑜 |
| 3 | | c0 3915 |
. . . . . 6
class
∅ |
| 4 | | cgoe 31315 |
. . . . . 6
class
∈𝑔 |
| 5 | 2, 3, 4 | co 6650 |
. . . . 5
class
(2𝑜∈𝑔∅) |
| 6 | | c1o 7553 |
. . . . . 6
class
1𝑜 |
| 7 | 2, 6, 4 | co 6650 |
. . . . 5
class
(2𝑜∈𝑔1𝑜) |
| 8 | | cgob 31332 |
. . . . 5
class
↔𝑔 |
| 9 | 5, 7, 8 | co 6650 |
. . . 4
class
((2𝑜∈𝑔∅)
↔𝑔
(2𝑜∈𝑔1𝑜)) |
| 10 | 9, 2 | cgol 31317 |
. . 3
class
∀𝑔2𝑜((2𝑜∈𝑔∅)
↔𝑔
(2𝑜∈𝑔1𝑜)) |
| 11 | | cgoq 31333 |
. . . 4
class
=𝑔 |
| 12 | 3, 6, 11 | co 6650 |
. . 3
class
(∅=𝑔1𝑜) |
| 13 | | cgoi 31330 |
. . 3
class
→𝑔 |
| 14 | 10, 12, 13 | co 6650 |
. 2
class
(∀𝑔2𝑜((2𝑜∈𝑔∅)
↔𝑔 (2𝑜∈𝑔1𝑜))
→𝑔 (∅=𝑔1𝑜)) |
| 15 | 1, 14 | wceq 1483 |
1
wff AxExt =
(∀𝑔2𝑜((2𝑜∈𝑔∅)
↔𝑔 (2𝑜∈𝑔1𝑜))
→𝑔 (∅=𝑔1𝑜)) |
