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Mirrors > Home > HSE Home > Th. List > hocofi | Structured version Visualization version Unicode version |
Description: Mapping of composition of Hilbert space operators. (Contributed by NM, 14-Nov-2000.) (New usage is discouraged.) |
Ref | Expression |
---|---|
hoeq.1 | |
hoeq.2 |
Ref | Expression |
---|---|
hocofi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hoeq.1 | . 2 | |
2 | hoeq.2 | . 2 | |
3 | fco 6058 | . 2 | |
4 | 1, 2, 3 | mp2an 708 | 1 |
Colors of variables: wff setvar class |
Syntax hints: ccom 5118 wf 5884 chil 27776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-fun 5890 df-fn 5891 df-f 5892 |
This theorem is referenced by: hocofni 28626 hocadddiri 28638 hocsubdiri 28639 ho2coi 28640 ho0coi 28647 hoid1i 28648 hoid1ri 28649 hoddii 28848 lnopcoi 28862 bdopcoi 28957 adjcoi 28959 nmopcoadji 28960 unierri 28963 pjsdii 29014 pjddii 29015 pjsdi2i 29016 pjss1coi 29022 pjss2coi 29023 pjorthcoi 29028 pjinvari 29050 pjclem1 29054 pjclem4 29058 pjadj2coi 29063 pj3lem1 29065 pj3si 29066 pj3cor1i 29068 |
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