Definition df-prm 11789

Description: Define the set of prime numbers. (Contributed by Paul Chapman, 22-Jun-2011.)

Assertion

Ref	Expression
df-prm	|- Prime = { p e. NN | { n e. NN | n || p } ~~ 2o }

Distinct variable group:   n, p

Detailed syntax breakdown of Definition df-prm

Step	Hyp	Ref	Expression
1		cprime 11788	. 2 class Prime
2		vn	. . . . . . 7 setvar n
3	2	cv 1330	. . . . . 6 class n
4		vp	. . . . . . 7 setvar p
5	4	cv 1330	. . . . . 6 class p
6		cdvds 11493	. . . . . 6 class ||
7	3, 5, 6	wbr 3929	. . . . 5 wff n || p
8		cn 8720	. . . . 5 class NN
9	7, 2, 8	crab 2420	. . . 4 class { n e. NN | n || p }
10		c2o 6307	. . . 4 class 2o
11		cen 6632	. . . 4 class ~~
12	9, 10, 11	wbr 3929	. . 3 wff { n e. NN | n || p } ~~ 2o
13	12, 4, 8	crab 2420	. 2 class { p e. NN | { n e. NN | n || p } ~~ 2o }
14	1, 13	wceq 1331	1 wff Prime = { p e. NN | { n e. NN | n || p } ~~ 2o }

This definition is referenced by:  isprm  11790