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Theorem itgoval 27345
 Description: Value of the integral-over function. (Contributed by Stefan O'Rear, 27-Nov-2014.)
Assertion
Ref Expression
itgoval IntgOver Poly coeffdeg
Distinct variable group:   ,,

Proof of Theorem itgoval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cnex 9073 . . 3
21elpw2 4366 . 2
3 fveq2 5730 . . . . 5 Poly Poly
43rexeqdv 2913 . . . 4 Poly coeffdeg Poly coeffdeg
54rabbidv 2950 . . 3 Poly coeffdeg Poly coeffdeg
6 df-itgo 27343 . . 3 IntgOver Poly coeffdeg
71rabex 4356 . . 3 Poly coeffdeg
85, 6, 7fvmpt 5808 . 2 IntgOver Poly coeffdeg
92, 8sylbir 206 1 IntgOver Poly coeffdeg
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wrex 2708  crab 2711   wss 3322  cpw 3801  cfv 5456  cc 8990  cc0 8992  c1 8993  Polycply 20105  coeffccoe 20107  degcdgr 20108  IntgOvercitgo 27341 This theorem is referenced by:  aaitgo  27346  itgoss  27347  itgocn  27348 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405  ax-cnex 9048 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-iota 5420  df-fun 5458  df-fv 5464  df-itgo 27343
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