Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > unitsscn | Structured version Visualization version GIF version |
Description: The closed unit is a subset of the set of the complex numbers Useful lemma for manipulating probabilities within the closed unit. (Contributed by Thierry Arnoux, 12-Dec-2016.) |
Ref | Expression |
---|---|
unitsscn | ⊢ (0[,]1) ⊆ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unitssre 12319 | . 2 ⊢ (0[,]1) ⊆ ℝ | |
2 | ax-resscn 9993 | . 2 ⊢ ℝ ⊆ ℂ | |
3 | 1, 2 | sstri 3612 | 1 ⊢ (0[,]1) ⊆ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3574 (class class class)co 6650 ℂcc 9934 ℝcr 9935 0cc0 9936 1c1 9937 [,]cicc 12178 |
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-8 1992 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-pow 4843 ax-pr 4906 ax-un 6949 ax-cnex 9992 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-i2m1 10004 ax-1ne0 10005 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 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-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-po 5035 df-so 5036 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-xr 10078 df-ltxr 10079 df-le 10080 df-icc 12182 |
This theorem is referenced by: iistmd 29948 xrge0iifhom 29983 xrge0iifmhm 29985 xrge0pluscn 29986 probdif 30482 cndprobin 30496 bayesth 30501 circlemeth 30718 |
Copyright terms: Public domain | W3C validator |