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Theorem hocofi 23261
Description: Mapping of composition of Hilbert space operators. (Contributed by NM, 14-Nov-2000.) (New usage is discouraged.)
Hypotheses
Ref Expression
hoeq.1  |-  S : ~H
--> ~H
hoeq.2  |-  T : ~H
--> ~H
Assertion
Ref Expression
hocofi  |-  ( S  o.  T ) : ~H --> ~H

Proof of Theorem hocofi
StepHypRef Expression
1 hoeq.1 . 2  |-  S : ~H
--> ~H
2 hoeq.2 . 2  |-  T : ~H
--> ~H
3 fco 5592 . 2  |-  ( ( S : ~H --> ~H  /\  T : ~H --> ~H )  ->  ( S  o.  T
) : ~H --> ~H )
41, 2, 3mp2an 654 1  |-  ( S  o.  T ) : ~H --> ~H
Colors of variables: wff set class
Syntax hints:    o. ccom 4874   -->wf 5442   ~Hchil 22414
This theorem is referenced by:  hocofni  23262  hocadddiri  23274  hocsubdiri  23275  ho2coi  23276  ho0coi  23283  hoid1i  23284  hoid1ri  23285  hoddii  23484  lnopcoi  23498  bdopcoi  23593  adjcoi  23595  nmopcoadji  23596  unierri  23599  pjsdii  23650  pjddii  23651  pjsdi2i  23652  pjss1coi  23658  pjss2coi  23659  pjorthcoi  23664  pjinvari  23686  pjclem1  23690  pjclem4  23694  pjadj2coi  23699  pj3lem1  23701  pj3si  23702  pj3cor1i  23704
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-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-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-fun 5448  df-fn 5449  df-f 5450
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