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Theorem dya2iocival 29168
 Description: The function returns closed-below open-above dyadic rational intervals covering the real line. This is the same construction as in dyadmbl 22637. (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 6315 . . . 4
2 oveq1 6315 . . . . 5
32oveq1d 6323 . . . 4
41, 3oveq12d 6326 . . 3
5 oveq2 6316 . . . . 5
65oveq2d 6324 . . . 4
75oveq2d 6324 . . . 4
86, 7oveq12d 6326 . . 3
9 dya2ioc.1 . . . 4
10 oveq1 6315 . . . . . 6
11 oveq1 6315 . . . . . . 7
1211oveq1d 6323 . . . . . 6
1310, 12oveq12d 6326 . . . . 5
14 oveq2 6316 . . . . . . 7
1514oveq2d 6324 . . . . . 6
1614oveq2d 6324 . . . . . 6
1715, 16oveq12d 6326 . . . . 5
1813, 17cbvmpt2v 6390 . . . 4
199, 18eqtr4i 2496 . . 3
20 ovex 6336 . . 3
214, 8, 19, 20ovmpt2 6451 . 2
2221ancoms 460 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376   wceq 1452   wcel 1904   crn 4840  cfv 5589  (class class class)co 6308   cmpt2 6310  c1 9558   caddc 9560   cdiv 10291  c2 10681  cz 10961  cioo 11660  cico 11662  cexp 12310  ctg 15414 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-iota 5553  df-fun 5591  df-fv 5597  df-ov 6311  df-oprab 6312  df-mpt2 6313 This theorem is referenced by:  dya2iocress  29169  dya2iocbrsiga  29170  dya2icoseg  29172
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