Definition df-fac 10313

Description: Define the factorial function on nonnegative integers. For example, ( ! ` 5 ) = 1 2 0 because 1 x. 2 x. 3 x. 4 x. 5 = 1 2 0 (ex-fac 12543). In the literature, the factorial function is written as a postscript exclamation point. (Contributed by NM, 2-Dec-2004.)

Assertion

Ref	Expression
df-fac	|- ! = ( { <. 0 , 1 >. } u. seq 1 ( x. , _I ) )

Detailed syntax breakdown of Definition df-fac

Step	Hyp	Ref	Expression
1		cfa 10312	. 2 class !
2		cc0 7500	. . . . 5 class 0
3		c1 7501	. . . . 5 class 1
4	2, 3	cop 3477	. . . 4 class <. 0 , 1 >.
5	4	csn 3474	. . 3 class { <. 0 , 1 >. }
6		cmul 7505	. . . 4 class x.
7		cid 4148	. . . 4 class _I
8	6, 7, 3	cseq 10059	. . 3 class seq 1 ( x. , _I )
9	5, 8	cun 3019	. 2 class ( { <. 0 , 1 >. } u. seq 1 ( x. , _I ) )
10	1, 9	wceq 1299	1 wff ! = ( { <. 0 , 1 >. } u. seq 1 ( x. , _I ) )

This definition is referenced by:  facnn  10314  fac0  10315