Definition df-fac 9653

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 10565). 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 , CC ) )

Detailed syntax breakdown of Definition df-fac

Step	Hyp	Ref	Expression
1		cfa 9652	. 2 class !
2		cc0 6981	. . . . 5 class 0
3		c1 6982	. . . . 5 class 1
4	2, 3	cop 3401	. . . 4 class <. 0 , 1 >.
5	4	csn 3398	. . 3 class { <. 0 , 1 >. }
6		cmul 6986	. . . 4 class x.
7		cc 6979	. . . 4 class CC
8		cid 4043	. . . 4 class _I
9	6, 7, 8, 3	cseq 9431	. . 3 class seq 1 ( x. , _I , CC )
10	5, 9	cun 2971	. 2 class ( { <. 0 , 1 >. } u. seq 1 ( x. , _I , CC ) )
11	1, 10	wceq 1284	1 wff ! = ( { <. 0 , 1 >. } u. seq 1 ( x. , _I , CC ) )

This definition is referenced by:  facnn  9654  fac0  9655