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Theorem specval 26640
 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 9585 . . 3
21rabex 4604 . 2
3 ax-hilex 25739 . 2
4 oveq1 6302 . . . . 5
5 f1eq1 5782 . . . . 5
64, 5syl 16 . . . 4
76notbid 294 . . 3
87rabbidv 3110 . 2
9 df-spec 26597 . 2
102, 3, 3, 8, 9fvmptmap 7467 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wceq 1379  crab 2821   cid 4796   cres 5007  wf 5590  wf1 5591  cfv 5594  (class class class)co 6295  cc 9502  chil 25659   chot 25679   chod 25680  cspc 25701 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692  ax-un 6587  ax-cnex 9560  ax-hilex 25739 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-pw 4018  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-mpt 4513  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-rn 5016  df-iota 5557  df-fun 5596  df-fn 5597  df-f 5598  df-f1 5599  df-fv 5602  df-ov 6298  df-oprab 6299  df-mpt2 6300  df-map 7434  df-spec 26597 This theorem is referenced by:  speccl  26641
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