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Theorem hocofni 23262
 Description: Functionality of composition of Hilbert space operators. (Contributed by NM, 12-Nov-2000.) (New usage is discouraged.)
Hypotheses
Ref Expression
hoeq.1
hoeq.2
Assertion
Ref Expression
hocofni

Proof of Theorem hocofni
StepHypRef Expression
1 hoeq.1 . . 3
2 hoeq.2 . . 3
31, 2hocofi 23261 . 2
4 ffn 5583 . 2
53, 4ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   ccom 4874   wfn 5441  wf 5442  chil 22414 This theorem is referenced by:  pjcofni  23657  pjinvari  23686  pj3si  23702 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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