Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-bc Unicode version

Definition df-bc 11194
 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 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 11193 . 2
2 vn . . 3
3 vk . . 3
4 cn0 9844 . . 3
5 cz 9903 . . 3
63cv 1618 . . . . 5
7 cc0 8617 . . . . . 6
82cv 1618 . . . . . 6
9 cfz 10660 . . . . . 6
107, 8, 9co 5710 . . . . 5
116, 10wcel 1621 . . . 4
12 cfa 11166 . . . . . 6
138, 12cfv 4592 . . . . 5
14 cmin 8917 . . . . . . . 8
158, 6, 14co 5710 . . . . . . 7
1615, 12cfv 4592 . . . . . 6
176, 12cfv 4592 . . . . . 6
18 cmul 8622 . . . . . 6
1916, 17, 18co 5710 . . . . 5
20 cdiv 9303 . . . . 5
2113, 19, 20co 5710 . . . 4
2211, 21, 7cif 3470 . . 3
232, 3, 4, 5, 22cmpt2 5712 . 2
241, 23wceq 1619 1
 Colors of variables: wff set class This definition is referenced by:  bcval  11195
 Copyright terms: Public domain W3C validator