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Mirrors > Home > HSE Home > Th. List > chex | Structured version Visualization version GIF version |
Description: The set of closed subspaces of a Hilbert space exists (is a set). (Contributed by NM, 23-Oct-1999.) (New usage is discouraged.) |
Ref | Expression |
---|---|
chex | ⊢ Cℋ ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shex 31240 | . 2 ⊢ Sℋ ∈ V | |
2 | chsssh 31253 | . 2 ⊢ Cℋ ⊆ Sℋ | |
3 | 1, 2 | ssexi 5327 | 1 ⊢ Cℋ ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 Vcvv 3477 Sℋ csh 30956 Cℋ cch 30957 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 ax-sep 5301 ax-pow 5370 ax-hilex 31027 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1539 df-fal 1549 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-rab 3433 df-v 3479 df-dif 3965 df-un 3967 df-in 3969 df-ss 3979 df-nul 4339 df-if 4531 df-pw 4606 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4912 df-br 5148 df-opab 5210 df-xp 5694 df-cnv 5696 df-dm 5698 df-rn 5699 df-res 5700 df-ima 5701 df-iota 6515 df-fv 6570 df-ov 7433 df-sh 31235 df-ch 31249 |
This theorem is referenced by: isst 32241 ishst 32242 |
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