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Definition df-tc 9167
Description: The transitive closure function. (Contributed by Mario Carneiro, 23-Jun-2013.)
Assertion
Ref Expression
df-tc TC = (𝑥 ∈ V ↦ {𝑦 ∣ (𝑥𝑦 ∧ Tr 𝑦)})
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-tc
StepHypRef Expression
1 ctc 9166 . 2 class TC
2 vx . . 3 setvar 𝑥
3 cvv 3444 . . 3 class V
42cv 1537 . . . . . . 7 class 𝑥
5 vy . . . . . . . 8 setvar 𝑦
65cv 1537 . . . . . . 7 class 𝑦
74, 6wss 3884 . . . . . 6 wff 𝑥𝑦
86wtr 5139 . . . . . 6 wff Tr 𝑦
97, 8wa 399 . . . . 5 wff (𝑥𝑦 ∧ Tr 𝑦)
109, 5cab 2779 . . . 4 class {𝑦 ∣ (𝑥𝑦 ∧ Tr 𝑦)}
1110cint 4841 . . 3 class {𝑦 ∣ (𝑥𝑦 ∧ Tr 𝑦)}
122, 3, 11cmpt 5113 . 2 class (𝑥 ∈ V ↦ {𝑦 ∣ (𝑥𝑦 ∧ Tr 𝑦)})
131, 12wceq 1538 1 wff TC = (𝑥 ∈ V ↦ {𝑦 ∣ (𝑥𝑦 ∧ Tr 𝑦)})
Colors of variables: wff setvar class
This definition is referenced by:  tcvalg  9168
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