Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > sitgf | Structured version Visualization version Unicode version |
Description: The integral for simple functions is itself a function. (Contributed by Thierry Arnoux, 13-Feb-2018.) |
Ref | Expression |
---|---|
sitgval.b | |
sitgval.j | |
sitgval.s | sigaGen |
sitgval.0 | |
sitgval.x | |
sitgval.h | RRHomScalar |
sitgval.1 | |
sitgval.2 | measures |
sitgf.1 | sitg sitg |
Ref | Expression |
---|---|
sitgf | sitg sitg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funmpt 5926 | . . . 4 MblFnM g | |
2 | sitgval.b | . . . . . 6 | |
3 | sitgval.j | . . . . . 6 | |
4 | sitgval.s | . . . . . 6 sigaGen | |
5 | sitgval.0 | . . . . . 6 | |
6 | sitgval.x | . . . . . 6 | |
7 | sitgval.h | . . . . . 6 RRHomScalar | |
8 | sitgval.1 | . . . . . 6 | |
9 | sitgval.2 | . . . . . 6 measures | |
10 | 2, 3, 4, 5, 6, 7, 8, 9 | sitgval 30394 | . . . . 5 sitg MblFnM g |
11 | 10 | funeqd 5910 | . . . 4 sitg MblFnM g |
12 | 1, 11 | mpbiri 248 | . . 3 sitg |
13 | funfn 5918 | . . 3 sitg sitg sitg | |
14 | 12, 13 | sylib 208 | . 2 sitg sitg |
15 | sitgf.1 | . . . 4 sitg sitg | |
16 | 15 | ralrimiva 2966 | . . 3 sitgsitg |
17 | fnfvrnss 6390 | . . 3 sitg sitg sitgsitg sitg | |
18 | 14, 16, 17 | syl2anc 693 | . 2 sitg |
19 | df-f 5892 | . 2 sitg sitg sitg sitg sitg | |
20 | 14, 18, 19 | sylanbrc 698 | 1 sitg sitg |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 crab 2916 cdif 3571 wss 3574 csn 4177 cuni 4436 cmpt 4729 ccnv 5113 cdm 5114 crn 5115 cima 5117 wfun 5882 wfn 5883 wf 5884 cfv 5888 (class class class)co 6650 cfn 7955 cc0 9936 cpnf 10071 cico 12177 cbs 15857 Scalarcsca 15944 cvsca 15945 ctopn 16082 c0g 16100 g cgsu 16101 RRHomcrrh 30037 sigaGencsigagen 30201 measurescmeas 30258 MblFnMcmbfm 30312 sitgcsitg 30391 |
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-rep 4771 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 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-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 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-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-sitg 30392 |
This theorem is referenced by: (None) |
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