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Mirrors > Home > MPE Home > Th. List > df-q | Structured version Visualization version GIF version |
Description: Define the set of rational numbers. Based on definition of rationals in [Apostol] p. 22. See elq 12699 for the relation "is rational". (Contributed by NM, 8-Jan-2002.) |
Ref | Expression |
---|---|
df-q | ⊢ ℚ = ( / “ (ℤ × ℕ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cq 12697 | . 2 class ℚ | |
2 | cdiv 11641 | . . 3 class / | |
3 | cz 12328 | . . . 4 class ℤ | |
4 | cn 11982 | . . . 4 class ℕ | |
5 | 3, 4 | cxp 5588 | . . 3 class (ℤ × ℕ) |
6 | 2, 5 | cima 5593 | . 2 class ( / “ (ℤ × ℕ)) |
7 | 1, 6 | wceq 1539 | 1 wff ℚ = ( / “ (ℤ × ℕ)) |
Colors of variables: wff setvar class |
This definition is referenced by: elq 12699 |
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