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Theorem eigvecval 27525
 Description: The set of eigenvectors of a Hilbert space operator. (Contributed by NM, 11-Mar-2006.) (Revised by Mario Carneiro, 16-Nov-2013.) (New usage is discouraged.)
Assertion
Ref Expression
eigvecval
Distinct variable group:   ,,

Proof of Theorem eigvecval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-hilex 26628 . . . 4
2 difexg 4565 . . . 4
31, 2ax-mp 5 . . 3
43rabex 4568 . 2
5 fveq1 5872 . . . . 5
65eqeq1d 2422 . . . 4
76rexbidv 2937 . . 3
87rabbidv 3070 . 2
9 df-eigvec 27482 . 2
104, 1, 1, 8, 9fvmptmap 7508 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437   wcel 1867  wrex 2774  crab 2777  cvv 3078   cdif 3430  wf 5589  cfv 5593  (class class class)co 6297  cc 9533  chil 26548   csm 26550  c0h 26564  cei 26588 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-8 1869  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4540  ax-nul 4548  ax-pow 4595  ax-pr 4653  ax-un 6589  ax-hilex 26628 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-sbc 3297  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-pw 3978  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-br 4418  df-opab 4477  df-mpt 4478  df-id 4761  df-xp 4852  df-rel 4853  df-cnv 4854  df-co 4855  df-dm 4856  df-rn 4857  df-iota 5557  df-fun 5595  df-fn 5596  df-f 5597  df-fv 5601  df-ov 6300  df-oprab 6301  df-mpt2 6302  df-map 7474  df-eigvec 27482 This theorem is referenced by:  eleigvec  27586
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