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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 6790 | 1 ⊢ 𝑋 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ∈ wcel 2106 Vcvv 3431 ‘cfv 6435 BaseSetcba 28945 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2709 ax-nul 5232 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-tru 1542 df-fal 1552 df-ex 1783 df-nf 1787 df-sb 2068 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2816 df-ral 3069 df-rex 3070 df-v 3433 df-dif 3891 df-un 3893 df-in 3895 df-ss 3905 df-nul 4259 df-sn 4564 df-pr 4566 df-uni 4842 df-iota 6393 df-fv 6443 |
This theorem is referenced by: h2hcau 29338 h2hlm 29339 axhilex-zf 29340 |
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