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Theorem hmopex 24958
Description: The class of Hermitian operators is a set. (Contributed by NM, 17-Aug-2006.) (New usage is discouraged.)
Assertion
Ref Expression
hmopex

Proof of Theorem hmopex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ovex 6086 . 2
2 hmopf 24957 . . . 4
3 ax-hilex 24080 . . . . 5
43, 3elmap 7200 . . . 4
52, 4sylibr 206 . . 3
65ssriv 3337 . 2
71, 6ssexi 4412 1
Colors of variables: wff setvar class
Syntax hints:  e.wcel 1749   cvv 2951  -->wf 5386  (class class class)co 6061   cmap 7175   chil 24000   cho 24031
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-8 1751  ax-9 1753  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403  ax-sep 4388  ax-nul 4396  ax-pow 4442  ax-pr 4503  ax-un 6342  ax-hilex 24080
This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-3an 952  df-tru 1355  df-ex 1582  df-nf 1585  df-sb 1694  df-eu 2248  df-mo 2249  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-ral 2699  df-rex 2700  df-rab 2703  df-v 2953  df-sbc 3165  df-dif 3308  df-un 3310  df-in 3312  df-ss 3319  df-nul 3615  df-if 3769  df-pw 3839  df-sn 3859  df-pr 3860  df-op 3862  df-uni 4067  df-br 4268  df-opab 4326  df-id 4607  df-xp 4817  df-rel 4818  df-cnv 4819  df-co 4820  df-dm 4821  df-rn 4822  df-iota 5353  df-fun 5392  df-fn 5393  df-f 5394  df-fv 5398  df-ov 6064  df-oprab 6065  df-mpt2 6066  df-map 7177  df-hmop 24927
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