df-denom - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > df-denom		Unicode version

Definition df-denom 12116

Description: The canonical denominator of a rational is the denominator of the rational's reduced fraction representation (no common factors, denominator positive). (Contributed by Stefan O'Rear, 13-Sep-2014.)

**Assertion**
Ref	Expression
df-denom	denom $/\$

Distinct variable group:

**Detailed syntax breakdown of Definition df-denom**
Step	Hyp	Ref	Expression
1		cdenom 12114	. 2 denom
2		vy	. . 3
3		cq 9557	. . 3
4		vx	. . . . . . . . . 10
5	4	cv 1342	. . . . . . . . 9
6		c1st 6106	. . . . . . . . 9
7	5, 6	cfv 5188	. . . . . . . 8
8		c2nd 6107	. . . . . . . . 9
9	5, 8	cfv 5188	. . . . . . . 8
10		cgcd 11875	. . . . . . . 8
11	7, 9, 10	co 5842	. . . . . . 7
12		c1 7754	. . . . . . 7
13	11, 12	wceq 1343	. . . . . 6
14	2	cv 1342	. . . . . . 7
15		cdiv 8568	. . . . . . . 8
16	7, 9, 15	co 5842	. . . . . . 7
17	14, 16	wceq 1343	. . . . . 6
18	13, 17	wa 103	. . . . 5 $/\$
19		cz 9191	. . . . . 6
20		cn 8857	. . . . . 6
21	19, 20	cxp 4602	. . . . 5
22	18, 4, 21	crio 5797	. . . 4 $/\$
23	22, 8	cfv 5188	. . 3 $/\$
24	2, 3, 23	cmpt 4043	. 2 $/\$
25	1, 24	wceq 1343	1 denom $/\$

Colors of variables: wff set class

This definition is referenced by: qdenval 12118 fden 12123

W3C validator