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Theorem specval 23401
 Description: The value of the spectrum of an operator. (Contributed by NM, 11-Apr-2006.) (Revised by Mario Carneiro, 16-Nov-2013.) (New usage is discouraged.)
Assertion
Ref Expression
specval
Distinct variable group:   ,

Proof of Theorem specval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cnex 9071 . . 3
21rabex 4354 . 2
3 ax-hilex 22502 . 2
4 oveq1 6088 . . . . 5
5 f1eq1 5634 . . . . 5
64, 5syl 16 . . . 4
76notbid 286 . . 3
87rabbidv 2948 . 2
9 df-spec 23358 . 2
102, 3, 3, 8, 9fvmptmap 7050 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wceq 1652  crab 2709   cid 4493   cres 4880  wf 5450  wf1 5451  cfv 5454  (class class class)co 6081  cc 8988  chil 22422   chot 22442   chod 22443  cspc 22464 This theorem is referenced by:  speccl  23402 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701  ax-cnex 9046  ax-hilex 22502 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 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-map 7020  df-spec 23358
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