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Theorem eigvecval 23430
 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 22533 . . . 4
2 difexg 4380 . . . 4
31, 2ax-mp 5 . . 3
43rabex 4383 . 2
5 fveq1 5756 . . . . 5
65eqeq1d 2450 . . . 4
76rexbidv 2732 . . 3
87rabbidv 2954 . 2
9 df-eigvec 23387 . 2
104, 1, 1, 8, 9fvmptmap 7079 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1727  wrex 2712  crab 2715  cvv 2962   cdif 3303  wf 5479  cfv 5483  (class class class)co 6110  cc 9019  chil 22453   csm 22455  c0h 22469  cei 22493 This theorem is referenced by:  eleigvec  23491 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-13 1729  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pow 4406  ax-pr 4432  ax-un 4730  ax-hilex 22533 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 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-sbc 3168  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-pw 3825  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-opab 4292  df-mpt 4293  df-id 4527  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-rn 4918  df-iota 5447  df-fun 5485  df-fn 5486  df-f 5487  df-fv 5491  df-ov 6113  df-oprab 6114  df-mpt2 6115  df-map 7049  df-eigvec 23387
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