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Theorem hmoval 22303
 Description: The set of Hermitian (self-adjoint) operators on a normed complex vector space. (Contributed by NM, 26-Jan-2008.) (Revised by Mario Carneiro, 16-Nov-2013.) (New usage is discouraged.)
Hypotheses
Ref Expression
hmoval.8
hmoval.9
Assertion
Ref Expression
hmoval
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem hmoval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 hmoval.8 . 2
2 oveq12 6082 . . . . . . 7
32anidms 627 . . . . . 6
4 hmoval.9 . . . . . 6
53, 4syl6eqr 2485 . . . . 5
65dmeqd 5064 . . . 4
75fveq1d 5722 . . . . 5
87eqeq1d 2443 . . . 4
96, 8rabeqbidv 2943 . . 3
10 df-hmo 22244 . . 3
11 ovex 6098 . . . . . 6
124, 11eqeltri 2505 . . . . 5
1312dmex 5124 . . . 4
1413rabex 4346 . . 3
159, 10, 14fvmpt 5798 . 2
161, 15syl5eq 2479 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  crab 2701  cvv 2948   cdm 4870  cfv 5446  (class class class)co 6073  cnv 22055  caj 22241  chmo 22242 This theorem is referenced by:  ishmo  22304 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 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-rab 2706  df-v 2950  df-sbc 3154  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-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-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076  df-hmo 22244
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