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Mirrors > Home > ILE Home > Th. List > df-fac | GIF version |
Description: Define the factorial function on nonnegative integers. For example, (!‘5) = 120 because 1 · 2 · 3 · 4 · 5 = 120 (ex-fac 13722). In the literature, the factorial function is written as a postscript exclamation point. (Contributed by NM, 2-Dec-2004.) |
Ref | Expression |
---|---|
df-fac | ⊢ ! = ({〈0, 1〉} ∪ seq1( · , I )) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfa 10646 | . 2 class ! | |
2 | cc0 7761 | . . . . 5 class 0 | |
3 | c1 7762 | . . . . 5 class 1 | |
4 | 2, 3 | cop 3584 | . . . 4 class 〈0, 1〉 |
5 | 4 | csn 3581 | . . 3 class {〈0, 1〉} |
6 | cmul 7766 | . . . 4 class · | |
7 | cid 4271 | . . . 4 class I | |
8 | 6, 7, 3 | cseq 10388 | . . 3 class seq1( · , I ) |
9 | 5, 8 | cun 3119 | . 2 class ({〈0, 1〉} ∪ seq1( · , I )) |
10 | 1, 9 | wceq 1348 | 1 wff ! = ({〈0, 1〉} ∪ seq1( · , I )) |
Colors of variables: wff set class |
This definition is referenced by: facnn 10648 fac0 10649 |
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