MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-fac Structured version   Visualization version   GIF version

Definition df-fac 13253
Description: Define the factorial function on nonnegative integers. For example, (!‘5) = 120 because 1 · 2 · 3 · 4 · 5 = 120 (ex-fac 27617). 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
StepHypRef Expression
1 cfa 13252 . 2 class !
2 cc0 10126 . . . . 5 class 0
3 c1 10127 . . . . 5 class 1
42, 3cop 4325 . . . 4 class ⟨0, 1⟩
54csn 4319 . . 3 class {⟨0, 1⟩}
6 cmul 10131 . . . 4 class ·
7 cid 5171 . . . 4 class I
86, 7, 3cseq 12993 . . 3 class seq1( · , I )
95, 8cun 3711 . 2 class ({⟨0, 1⟩} ∪ seq1( · , I ))
101, 9wceq 1630 1 wff ! = ({⟨0, 1⟩} ∪ seq1( · , I ))
Colors of variables: wff setvar class
This definition is referenced by:  facnn  13254  fac0  13255
  Copyright terms: Public domain W3C validator