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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 6677 | 1 ⊢ 𝑋 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∈ wcel 2105 Vcvv 3492 ‘cfv 6348 BaseSetcba 28290 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-nul 5201 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-v 3494 df-sbc 3770 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-sn 4558 df-pr 4560 df-uni 4831 df-iota 6307 df-fv 6356 |
This theorem is referenced by: h2hcau 28683 h2hlm 28684 axhilex-zf 28685 |
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