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Definition df-bc 12381
Description: Define the binomial coefficient operation. 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 0 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 12380 . 2
2 vn . . 3
3 vk . . 3
4 cn0 10820 . . 3
5 cz 10889 . . 3
63cv 1394 . . . . 5
7 cc0 9513 . . . . . 6
82cv 1394 . . . . . 6
9 cfz 11701 . . . . . 6
107, 8, 9co 6296 . . . . 5
116, 10wcel 1818 . . . 4
12 cfa 12353 . . . . . 6
138, 12cfv 5593 . . . . 5
14 cmin 9828 . . . . . . . 8
158, 6, 14co 6296 . . . . . . 7
1615, 12cfv 5593 . . . . . 6
176, 12cfv 5593 . . . . . 6
18 cmul 9518 . . . . . 6
1916, 17, 18co 6296 . . . . 5
20 cdiv 10231 . . . . 5
2113, 19, 20co 6296 . . . 4
2211, 21, 7cif 3941 . . 3
232, 3, 4, 5, 22cmpt2 6298 . 2
241, 23wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  bcval  12382
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