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Mirrors > Home > ILE Home > Th. List > df-int | GIF version |
Description: Define the intersection of a class. Definition 7.35 of [TakeutiZaring] p. 44. For example, ∩ { { 1 , 3 } , { 1 , 8 } } = { 1 } . Compare this with the intersection of two classes, df-in 2918. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
df-int | ⊢ ∩ A = {x ∣ ∀y(y ∈ A → x ∈ y)} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class A | |
2 | 1 | cint 3606 | . 2 class ∩ A |
3 | vy | . . . . . . 7 setvar y | |
4 | 3 | cv 1241 | . . . . . 6 class y |
5 | 4, 1 | wcel 1390 | . . . . 5 wff y ∈ A |
6 | vx | . . . . . 6 setvar x | |
7 | 6, 3 | wel 1391 | . . . . 5 wff x ∈ y |
8 | 5, 7 | wi 4 | . . . 4 wff (y ∈ A → x ∈ y) |
9 | 8, 3 | wal 1240 | . . 3 wff ∀y(y ∈ A → x ∈ y) |
10 | 9, 6 | cab 2023 | . 2 class {x ∣ ∀y(y ∈ A → x ∈ y)} |
11 | 2, 10 | wceq 1242 | 1 wff ∩ A = {x ∣ ∀y(y ∈ A → x ∈ y)} |
Colors of variables: wff set class |
This definition is referenced by: dfint2 3608 elint 3612 int0 3620 dfiin2g 3681 bdcint 9332 bdcriota 9338 |
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