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Theorem idunop 23473
 Description: The identity function (restricted to Hilbert space) is a unitary operator. (Contributed by NM, 21-Jan-2006.) (New usage is discouraged.)
Assertion
Ref Expression
idunop

Proof of Theorem idunop
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 f1oi 5705 . . 3
2 f1ofo 5673 . . 3
31, 2ax-mp 8 . 2
4 fvresi 5916 . . . 4
5 fvresi 5916 . . . 4
64, 5oveqan12d 6092 . . 3
76rgen2a 2764 . 2
8 elunop 23367 . 2
93, 7, 8mpbir2an 887 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  wral 2697   cid 4485   cres 4872  wfo 5444  wf1o 5445  cfv 5446  (class class class)co 6073  chil 22414   csp 22417  cuo 22444 This theorem is referenced by:  idlnop  23487 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-rep 4312  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-hilex 22494 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-ov 6076  df-unop 23338
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