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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 6905 | 1 ⊢ 𝑋 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 ∈ wcel 2099 Vcvv 3469 ‘cfv 6542 BaseSetcba 30383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2698 ax-nul 5300 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-ne 2936 df-v 3471 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4319 df-sn 4625 df-pr 4627 df-uni 4904 df-iota 6494 df-fv 6550 |
This theorem is referenced by: h2hcau 30776 h2hlm 30777 axhilex-zf 30778 |
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