Hilbert Space Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HSE Home > Th. List > lnopfi | Structured version Visualization version GIF version |
Description: A linear Hilbert space operator is a Hilbert space operator. (Contributed by NM, 23-Jan-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
lnopl.1 | ⊢ 𝑇 ∈ LinOp |
Ref | Expression |
---|---|
lnopfi | ⊢ 𝑇: ℋ⟶ ℋ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lnopl.1 | . 2 ⊢ 𝑇 ∈ LinOp | |
2 | lnopf 29638 | . 2 ⊢ (𝑇 ∈ LinOp → 𝑇: ℋ⟶ ℋ) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝑇: ℋ⟶ ℋ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 ⟶wf 6353 ℋchba 28698 LinOpclo 28726 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 ax-sep 5205 ax-nul 5212 ax-pow 5268 ax-pr 5332 ax-un 7463 ax-hilex 28778 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ral 3145 df-rex 3146 df-rab 3149 df-v 3498 df-sbc 3775 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-pw 4543 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-opab 5131 df-id 5462 df-xp 5563 df-rel 5564 df-cnv 5565 df-co 5566 df-dm 5567 df-rn 5568 df-iota 6316 df-fun 6359 df-fn 6360 df-f 6361 df-fv 6365 df-ov 7161 df-oprab 7162 df-mpo 7163 df-map 8410 df-lnop 29620 |
This theorem is referenced by: lnopaddi 29750 lnopsubi 29753 hoddii 29768 nmlnop0iALT 29774 nmlnopgt0i 29776 lnopmi 29779 lnophsi 29780 lnophdi 29781 lnopcoi 29782 lnopco0i 29783 lnopeq0lem1 29784 lnopeq0i 29786 lnopeqi 29787 lnopunilem1 29789 lnopunilem2 29790 lnophmlem2 29796 lnophmi 29797 nmbdoplbi 29803 nmcopexi 29806 nmcoplbi 29807 lnopconi 29813 imaelshi 29837 rnelshi 29838 cnlnadjlem2 29847 cnlnadjlem6 29851 cnlnadjlem7 29852 cnlnadjeui 29856 nmopcoi 29874 bdopcoi 29877 hmopidmchi 29930 hmopidmpji 29931 |
Copyright terms: Public domain | W3C validator |