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Theorem elbdop 25199
 Description: Property defining a bounded linear Hilbert space operator. (Contributed by NM, 18-Jan-2006.) (Revised by Mario Carneiro, 16-Nov-2013.) (New usage is discouraged.)
Assertion
Ref Expression
elbdop

Proof of Theorem elbdop
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5688 . . 3
21breq1d 4299 . 2
3 df-bdop 25181 . 2
42, 3elrab2 3116 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1364   wcel 1761   class class class wbr 4289  cfv 5415   cpnf 9411   clt 9414  cnop 24282  clo 24284  cbo 24285 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-rex 2719  df-rab 2722  df-v 2972  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-nul 3635  df-if 3789  df-sn 3875  df-pr 3877  df-op 3881  df-uni 4089  df-br 4290  df-iota 5378  df-fv 5423  df-bdop 25181 This theorem is referenced by:  bdopln  25200  nmopre  25209  elbdop2  25210  0bdop  25332
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