Step | Hyp | Ref
| Expression |
1 | | cfinext 32385 |
. 2
class
/FinExt |
2 | | ve |
. . . . . 6
setvar 𝑒 |
3 | 2 | cv 1541 |
. . . . 5
class 𝑒 |
4 | | vf |
. . . . . 6
setvar 𝑓 |
5 | 4 | cv 1541 |
. . . . 5
class 𝑓 |
6 | | cfldext 32384 |
. . . . 5
class
/FldExt |
7 | 3, 5, 6 | wbr 5106 |
. . . 4
wff 𝑒/FldExt𝑓 |
8 | | cextdg 32387 |
. . . . . 6
class
[:] |
9 | 3, 5, 8 | co 7358 |
. . . . 5
class (𝑒[:]𝑓) |
10 | | cn0 12418 |
. . . . 5
class
ℕ0 |
11 | 9, 10 | wcel 2107 |
. . . 4
wff (𝑒[:]𝑓) ∈ ℕ0 |
12 | 7, 11 | wa 397 |
. . 3
wff (𝑒/FldExt𝑓 ∧ (𝑒[:]𝑓) ∈
ℕ0) |
13 | 12, 2, 4 | copab 5168 |
. 2
class
{⟨𝑒, 𝑓⟩ ∣ (𝑒/FldExt𝑓 ∧ (𝑒[:]𝑓) ∈
ℕ0)} |
14 | 1, 13 | wceq 1542 |
1
wff
/FinExt = {⟨𝑒, 𝑓⟩ ∣ (𝑒/FldExt𝑓 ∧ (𝑒[:]𝑓) ∈
ℕ0)} |