![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 6460 | 1 ⊢ 𝑋 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1601 ∈ wcel 2107 Vcvv 3398 ‘cfv 6135 BaseSetcba 28013 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 ax-ext 2754 ax-nul 5025 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-mo 2551 df-eu 2587 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-ral 3095 df-rex 3096 df-v 3400 df-sbc 3653 df-dif 3795 df-un 3797 df-in 3799 df-ss 3806 df-nul 4142 df-sn 4399 df-pr 4401 df-uni 4672 df-iota 6099 df-fv 6143 |
This theorem is referenced by: h2hcau 28408 h2hlm 28409 axhilex-zf 28410 |
Copyright terms: Public domain | W3C validator |