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Mirrors > Home > NFE Home > Th. List > df-qs | GIF version |
Description: Define quotient set. R is usually an equivalence relation. Definition of [Enderton] p. 58. (Contributed by set.mm contributors, 22-Feb-2015.) |
Ref | Expression |
---|---|
df-qs | ⊢ (A / R) = {y ∣ ∃x ∈ A y = [x]R} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class A | |
2 | cR | . . 3 class R | |
3 | 1, 2 | cqs 5946 | . 2 class (A / R) |
4 | vy | . . . . . 6 setvar y | |
5 | 4 | cv 1641 | . . . . 5 class y |
6 | vx | . . . . . . 7 setvar x | |
7 | 6 | cv 1641 | . . . . . 6 class x |
8 | 7, 2 | cec 5945 | . . . . 5 class [x]R |
9 | 5, 8 | wceq 1642 | . . . 4 wff y = [x]R |
10 | 9, 6, 1 | wrex 2615 | . . 3 wff ∃x ∈ A y = [x]R |
11 | 10, 4 | cab 2339 | . 2 class {y ∣ ∃x ∈ A y = [x]R} |
12 | 3, 11 | wceq 1642 | 1 wff (A / R) = {y ∣ ∃x ∈ A y = [x]R} |
Colors of variables: wff setvar class |
This definition is referenced by: qseq1 5974 qseq2 5975 elqsg 5976 qsexg 5982 uniqs 5984 snec 5987 |
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