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Theorem pntrval 21248
 Description: Define the residual of the second Chebyshev function. The goal is to have , or . (Contributed by Mario Carneiro, 8-Apr-2016.)
Hypothesis
Ref Expression
pntrval.r ψ
Assertion
Ref Expression
pntrval ψ
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem pntrval
StepHypRef Expression
1 fveq2 5720 . . 3 ψ ψ
2 id 20 . . 3
31, 2oveq12d 6091 . 2 ψ ψ
4 pntrval.r . 2 ψ
5 ovex 6098 . 2 ψ
63, 4, 5fvmpt 5798 1 ψ
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725   cmpt 4258  cfv 5446  (class class class)co 6073   cmin 9283  crp 10604  ψcchp 20867 This theorem is referenced by:  pntrmax  21250  pntrsumo1  21251  selbergr  21254  selberg3r  21255  selberg4r  21256  pntrlog2bndlem2  21264  pntrlog2bndlem4  21266  pntrlog2bnd  21270  pntpbnd1a  21271  pntibndlem2  21277  pntlem3  21295 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-mpt 4260  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
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