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Theorem dya2iocival 24615
 Description: The function returns closed below opened above dyadic rational intervals covering the the real line. This is the same construction as in dyadmbl 19484. (Contributed by Thierry Arnoux, 24-Sep-2017.)
Hypotheses
Ref Expression
sxbrsiga.0
dya2ioc.1
Assertion
Ref Expression
dya2iocival
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem dya2iocival
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq1 6080 . . . 4
2 oveq1 6080 . . . . 5
32oveq1d 6088 . . . 4
41, 3oveq12d 6091 . . 3
5 oveq2 6081 . . . . 5
65oveq2d 6089 . . . 4
75oveq2d 6089 . . . 4
86, 7oveq12d 6091 . . 3
9 dya2ioc.1 . . . 4
10 oveq1 6080 . . . . . 6
11 oveq1 6080 . . . . . . 7
1211oveq1d 6088 . . . . . 6
1310, 12oveq12d 6091 . . . . 5
14 oveq2 6081 . . . . . . 7
1514oveq2d 6089 . . . . . 6
1614oveq2d 6089 . . . . . 6
1715, 16oveq12d 6091 . . . . 5
1813, 17cbvmpt2v 6144 . . . 4
199, 18eqtr4i 2458 . . 3
20 ovex 6098 . . 3
214, 8, 19, 20ovmpt2 6201 . 2
2221ancoms 440 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   crn 4871  cfv 5446  (class class class)co 6073   cmpt2 6075  c1 8983   caddc 8985   cdiv 9669  c2 10041  cz 10274  cioo 10908  cico 10910  cexp 11374  ctg 13657 This theorem is referenced by:  dya2iocress  24616  dya2iocbrsiga  24617  dya2icoseg  24619 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076  df-oprab 6077  df-mpt2 6078
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