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Theorem bloln 22277
 Description: A bounded operator is a linear operator. (Contributed by NM, 8-Dec-2007.) (New usage is discouraged.)
Hypotheses
Ref Expression
bloln.4
bloln.5
Assertion
Ref Expression
bloln

Proof of Theorem bloln
StepHypRef Expression
1 eqid 2435 . . . 4
2 bloln.4 . . . 4
3 bloln.5 . . . 4
41, 2, 3isblo 22275 . . 3
54simprbda 607 . 2
653impa 1148 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725   class class class wbr 4204  cfv 5446  (class class class)co 6073   cpnf 9109   clt 9112  cnv 22055   clno 22233  cnmoo 22234   cblo 22235 This theorem is referenced by:  blof  22278  nmblolbii  22292  isblo3i  22294  blometi  22296  blocn2  22301  ubthlem2  22365 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-sep 4322  ax-nul 4330  ax-pr 4395 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-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076  df-oprab 6077  df-mpt2 6078  df-blo 22239
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