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| Mirrors > Home > MPE Home > Th. List > hlex | Structured version Visualization version GIF version | ||
| Description: The base set of a Hilbert space is a set. (Contributed by NM, 7-Sep-2007.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| hlex.1 | ⊢ 𝑋 = (BaseSet‘𝑈) | 
| Ref | Expression | 
|---|---|
| hlex | ⊢ 𝑋 ∈ V | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | hlex.1 | . 2 ⊢ 𝑋 = (BaseSet‘𝑈) | |
| 2 | 1 | fvexi 6919 | 1 ⊢ 𝑋 ∈ V | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1539 ∈ wcel 2107 Vcvv 3479 ‘cfv 6560 BaseSetcba 30606 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-nul 5305 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-ne 2940 df-v 3481 df-dif 3953 df-un 3955 df-ss 3967 df-nul 4333 df-sn 4626 df-pr 4628 df-uni 4907 df-iota 6513 df-fv 6568 | 
| This theorem is referenced by: h2hcau 30999 h2hlm 31000 axhilex-zf 31001 | 
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