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Theorem hmopex 25748
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 6247 . 2
2 hmopf 25747 . . . 4
3 ax-hilex 24870 . . . . 5
43, 3elmap 7375 . . . 4
52, 4sylibr 212 . . 3
65ssriv 3474 . 2
71, 6ssexi 4554 1
Colors of variables: wff setvar class
Syntax hints:  e.wcel 1758   cvv 3081  -->wf 5533  (class class class)co 6222   cmap 7348   chil 24790   cho 24821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4530  ax-nul 4538  ax-pow 4587  ax-pr 4648  ax-un 6505  ax-hilex 24870
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-rex 2806  df-rab 2809  df-v 3083  df-sbc 3298  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-pw 3978  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4209  df-br 4410  df-opab 4468  df-id 4753  df-xp 4963  df-rel 4964  df-cnv 4965  df-co 4966  df-dm 4967  df-rn 4968  df-iota 5500  df-fun 5539  df-fn 5540  df-f 5541  df-fv 5545  df-ov 6225  df-oprab 6226  df-mpt2 6227  df-map 7350  df-hmop 25717
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