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Mirrors > Home > MPE Home > Th. List > bcval3 | Structured version Visualization version Unicode version |
Description: Value of the binomial coefficient, choose , outside of its standard domain. Remark in [Gleason] p. 295. (Contributed by NM, 14-Jul-2005.) (Revised by Mario Carneiro, 8-Nov-2013.) |
Ref | Expression |
---|---|
bcval3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bcval 13091 | . . 3 | |
2 | 1 | 3adant3 1081 | . 2 |
3 | iffalse 4095 | . . 3 | |
4 | 3 | 3ad2ant3 1084 | . 2 |
5 | 2, 4 | eqtrd 2656 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 w3a 1037 wceq 1483 wcel 1990 cif 4086 cfv 5888 (class class class)co 6650 cc0 9936 cmul 9941 cmin 10266 cdiv 10684 cn0 11292 cz 11377 cfz 12326 cfa 13060 cbc 13089 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-mulcl 9998 ax-i2m1 10004 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-bc 13090 |
This theorem is referenced by: bcval4 13094 bccmpl 13096 bcval5 13105 bcpasc 13108 bccl 13109 hashbc 13237 binomlem 14561 bccbc 38544 |
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