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Mirrors > Home > ILE Home > Th. List > df-disj | GIF version |
Description: A collection of classes B(x) is disjoint when for each element y, it is in B(x) for at most one x. (Contributed by Mario Carneiro, 14-Nov-2016.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
df-disj | ⊢ (Disj x ∈ A B ↔ ∀y∃*x ∈ A y ∈ B) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vx | . . 3 setvar x | |
2 | cA | . . 3 class A | |
3 | cB | . . 3 class B | |
4 | 1, 2, 3 | wdisj 3736 | . 2 wff Disj x ∈ A B |
5 | vy | . . . . . 6 setvar y | |
6 | 5 | cv 1241 | . . . . 5 class y |
7 | 6, 3 | wcel 1390 | . . . 4 wff y ∈ B |
8 | 7, 1, 2 | wrmo 2303 | . . 3 wff ∃*x ∈ A y ∈ B |
9 | 8, 5 | wal 1240 | . 2 wff ∀y∃*x ∈ A y ∈ B |
10 | 4, 9 | wb 98 | 1 wff (Disj x ∈ A B ↔ ∀y∃*x ∈ A y ∈ B) |
Colors of variables: wff set class |
This definition is referenced by: dfdisj2 3738 disjss2 3739 cbvdisj 3746 nfdisj1 3749 |
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