Detailed syntax breakdown of Definition df-tc
Step | Hyp | Ref
| Expression |
1 | | ctc 8495 |
. 2
class
TC |
2 | | vx |
. . 3
setvar 𝑥 |
3 | | cvv 3173 |
. . 3
class
V |
4 | 2 | cv 1474 |
. . . . . . 7
class 𝑥 |
5 | | vy |
. . . . . . . 8
setvar 𝑦 |
6 | 5 | cv 1474 |
. . . . . . 7
class 𝑦 |
7 | 4, 6 | wss 3540 |
. . . . . 6
wff 𝑥 ⊆ 𝑦 |
8 | 6 | wtr 4680 |
. . . . . 6
wff Tr 𝑦 |
9 | 7, 8 | wa 383 |
. . . . 5
wff (𝑥 ⊆ 𝑦 ∧ Tr 𝑦) |
10 | 9, 5 | cab 2596 |
. . . 4
class {𝑦 ∣ (𝑥 ⊆ 𝑦 ∧ Tr 𝑦)} |
11 | 10 | cint 4410 |
. . 3
class ∩ {𝑦
∣ (𝑥 ⊆ 𝑦 ∧ Tr 𝑦)} |
12 | 2, 3, 11 | cmpt 4643 |
. 2
class (𝑥 ∈ V ↦ ∩ {𝑦
∣ (𝑥 ⊆ 𝑦 ∧ Tr 𝑦)}) |
13 | 1, 12 | wceq 1475 |
1
wff TC = (𝑥 ∈ V ↦ ∩ {𝑦
∣ (𝑥 ⊆ 𝑦 ∧ Tr 𝑦)}) |