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Definition df-fac 10479
Description: Define the factorial function on nonnegative integers. For example, (!‘5) = 120 because 1 · 2 · 3 · 4 · 5 = 120 (ex-fac 12970). 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 10478 . 2 class !
2 cc0 7627 . . . . 5 class 0
3 c1 7628 . . . . 5 class 1
42, 3cop 3530 . . . 4 class ⟨0, 1⟩
54csn 3527 . . 3 class {⟨0, 1⟩}
6 cmul 7632 . . . 4 class ·
7 cid 4210 . . . 4 class I
86, 7, 3cseq 10225 . . 3 class seq1( · , I )
95, 8cun 3069 . 2 class ({⟨0, 1⟩} ∪ seq1( · , I ))
101, 9wceq 1331 1 wff ! = ({⟨0, 1⟩} ∪ seq1( · , I ))
Colors of variables: wff set class
This definition is referenced by:  facnn  10480  fac0  10481
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