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Mirrors > Home > HSE Home > Th. List > bdopln | Structured version Visualization version Unicode version |
Description: A bounded linear Hilbert space operator is a linear operator. (Contributed by NM, 18-Feb-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bdopln |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elbdop 28719 | . 2 | |
2 | 1 | simplbi 476 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 class class class wbr 4653 cfv 5888 cpnf 10071 clt 10074 cnop 27802 clo 27804 cbo 27805 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 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-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-bdop 28701 |
This theorem is referenced by: bdopf 28721 nmbdoplbi 28883 bdophmi 28891 lncnopbd 28896 nmopcoi 28954 bdophsi 28955 bdopcoi 28957 nmopcoadj0i 28962 unierri 28963 |
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