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Definition df-fac 12875
Description: Define the factorial function on nonnegative integers. For example, (!‘5) = 120 because 1 · 2 · 3 · 4 · 5 = 120 (ex-fac 26463). 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 12874 . 2 class !
2 cc0 9789 . . . . 5 class 0
3 c1 9790 . . . . 5 class 1
42, 3cop 4127 . . . 4 class ⟨0, 1⟩
54csn 4121 . . 3 class {⟨0, 1⟩}
6 cmul 9794 . . . 4 class ·
7 cid 4935 . . . 4 class I
86, 7, 3cseq 12615 . . 3 class seq1( · , I )
95, 8cun 3534 . 2 class ({⟨0, 1⟩} ∪ seq1( · , I ))
101, 9wceq 1474 1 wff ! = ({⟨0, 1⟩} ∪ seq1( · , I ))
Colors of variables: wff setvar class
This definition is referenced by:  facnn  12876  fac0  12877
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