df-denom - Intuitionistic Logic Explorer

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Definition df-denom 12621

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 12619	. 2 denom
2		vy	. . 3
3		cq 9775	. . 3
4		vx	. . . . . . . . . 10
5	4	cv 1372	. . . . . . . . 9
6		c1st 6247	. . . . . . . . 9
7	5, 6	cfv 5290	. . . . . . . 8
8		c2nd 6248	. . . . . . . . 9
9	5, 8	cfv 5290	. . . . . . . 8
10		cgcd 12389	. . . . . . . 8
11	7, 9, 10	co 5967	. . . . . . 7
12		c1 7961	. . . . . . 7
13	11, 12	wceq 1373	. . . . . 6
14	2	cv 1372	. . . . . . 7
15		cdiv 8780	. . . . . . . 8
16	7, 9, 15	co 5967	. . . . . . 7
17	14, 16	wceq 1373	. . . . . 6
18	13, 17	wa 104	. . . . 5 $/\$
19		cz 9407	. . . . . 6
20		cn 9071	. . . . . 6
21	19, 20	cxp 4691	. . . . 5
22	18, 4, 21	crio 5921	. . . 4 $/\$
23	22, 8	cfv 5290	. . 3 $/\$
24	2, 3, 23	cmpt 4121	. 2 $/\$
25	1, 24	wceq 1373	1 denom $/\$

Colors of variables: wff set class

This definition is referenced by: qdenval 12623 fden 12628

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