df-denom - Intuitionistic Logic Explorer

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Definition df-denom 12184

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 12182	. 2 denom
2		vy	. . 3
3		cq 9619	. . 3
4		vx	. . . . . . . . . 10
5	4	cv 1352	. . . . . . . . 9
6		c1st 6139	. . . . . . . . 9
7	5, 6	cfv 5217	. . . . . . . 8
8		c2nd 6140	. . . . . . . . 9
9	5, 8	cfv 5217	. . . . . . . 8
10		cgcd 11943	. . . . . . . 8
11	7, 9, 10	co 5875	. . . . . . 7
12		c1 7812	. . . . . . 7
13	11, 12	wceq 1353	. . . . . 6
14	2	cv 1352	. . . . . . 7
15		cdiv 8629	. . . . . . . 8
16	7, 9, 15	co 5875	. . . . . . 7
17	14, 16	wceq 1353	. . . . . 6
18	13, 17	wa 104	. . . . 5 $/\$
19		cz 9253	. . . . . 6
20		cn 8919	. . . . . 6
21	19, 20	cxp 4625	. . . . 5
22	18, 4, 21	crio 5830	. . . 4 $/\$
23	22, 8	cfv 5217	. . 3 $/\$
24	2, 3, 23	cmpt 4065	. 2 $/\$
25	1, 24	wceq 1353	1 denom $/\$

Colors of variables: wff set class

This definition is referenced by: qdenval 12186 fden 12191

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