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Mirrors > Home > MPE Home > Th. List > Mathboxes > baselsiga | Structured version Visualization version Unicode version |
Description: A sigma-algebra contains its base universe set. (Contributed by Thierry Arnoux, 26-Oct-2016.) |
Ref | Expression |
---|---|
baselsiga | sigAlgebra |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3212 | . 2 sigAlgebra | |
2 | issiga 30174 | . . . 4 sigAlgebra | |
3 | 2 | simplbda 654 | . . 3 sigAlgebra |
4 | 3 | simp1d 1073 | . 2 sigAlgebra |
5 | 1, 4 | mpancom 703 | 1 sigAlgebra |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 wral 2912 cvv 3200 cdif 3571 wss 3574 cpw 4158 cuni 4436 class class class wbr 4653 cfv 5888 com 7065 cdom 7953 sigAlgebracsiga 30170 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-fal 1489 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-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-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-siga 30171 |
This theorem is referenced by: unielsiga 30191 sigaldsys 30222 cldssbrsiga 30250 1stmbfm 30322 2ndmbfm 30323 unveldomd 30477 probmeasb 30492 dstrvprob 30533 |
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