Definition df-fac 14313

Description: Define the factorial function on nonnegative integers. For example, (!‘5) = 120 because 1 · 2 · 3 · 4 · 5 = 120 (ex-fac 30470). 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⟩} ∪ seq1( · , I ))

Detailed syntax breakdown of Definition df-fac

Step	Hyp	Ref	Expression
1		cfa 14312	. 2 class !
2		cc0 11155	. . . . 5 class 0
3		c1 11156	. . . . 5 class 1
4	2, 3	cop 4632	. . . 4 class ⟨0, 1⟩
5	4	csn 4626	. . 3 class {⟨0, 1⟩}
6		cmul 11160	. . . 4 class ·
7		cid 5577	. . . 4 class I
8	6, 7, 3	cseq 14042	. . 3 class seq1( · , I )
9	5, 8	cun 3949	. 2 class ({⟨0, 1⟩} ∪ seq1( · , I ))
10	1, 9	wceq 1540	1 wff ! = ({⟨0, 1⟩} ∪ seq1( · , I ))

This definition is referenced by:  facnn  14314  fac0  14315