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Definition df-bc 9772
 Description: Define the binomial coefficient operation. For example, (ex-bc 10717). In the literature, this function is often written as a column vector of the two arguments, or with the arguments as subscripts before and after the letter "C". is read " choose ." Definition of binomial coefficient in [Gleason] p. 295. As suggested by Gleason, we define it to be 0 when does not hold. (Contributed by NM, 10-Jul-2005.)
Assertion
Ref Expression
df-bc
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-bc
StepHypRef Expression
1 cbc 9771 . 2
2 vn . . 3
3 vk . . 3
4 cn0 8355 . . 3
5 cz 8432 . . 3
63cv 1284 . . . . 5
7 cc0 7043 . . . . . 6
82cv 1284 . . . . . 6
9 cfz 9105 . . . . . 6
107, 8, 9co 5543 . . . . 5
116, 10wcel 1434 . . . 4
12 cfa 9749 . . . . . 6
138, 12cfv 4932 . . . . 5
14 cmin 7346 . . . . . . . 8
158, 6, 14co 5543 . . . . . . 7
1615, 12cfv 4932 . . . . . 6
176, 12cfv 4932 . . . . . 6
18 cmul 7048 . . . . . 6
1916, 17, 18co 5543 . . . . 5
20 cdiv 7827 . . . . 5
2113, 19, 20co 5543 . . . 4
2211, 21, 7cif 3359 . . 3
232, 3, 4, 5, 22cmpt2 5545 . 2
241, 23wceq 1285 1
 Colors of variables: wff set class This definition is referenced by:  bcval  9773
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