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Mirrors > Home > MPE Home > Th. List > Mathboxes > elprob | Structured version Visualization version Unicode version |
Description: The property of being a probability measure. (Contributed by Thierry Arnoux, 8-Dec-2016.) |
Ref | Expression |
---|---|
elprob | Prob measures |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . . . 4 | |
2 | dmeq 5324 | . . . . 5 | |
3 | 2 | unieqd 4446 | . . . 4 |
4 | 1, 3 | fveq12d 6197 | . . 3 |
5 | 4 | eqeq1d 2624 | . 2 |
6 | df-prob 30470 | . 2 Prob measures | |
7 | 5, 6 | elrab2 3366 | 1 Prob measures |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wcel 1990 cuni 4436 cdm 5114 crn 5115 cfv 5888 c1 9937 measurescmeas 30258 Probcprb 30469 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-rab 2921 df-v 3202 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-dm 5124 df-iota 5851 df-fv 5896 df-prob 30470 |
This theorem is referenced by: domprobmeas 30472 probtot 30474 probfinmeasbOLD 30490 probfinmeasb 30491 probmeasb 30492 dstrvprob 30533 |
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