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Mirrors > Home > HSE Home > Th. List > atelch | Structured version Visualization version GIF version |
Description: An atom is a Hilbert lattice element. (Contributed by NM, 22-Jun-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
atelch | ⊢ (𝐴 ∈ HAtoms → 𝐴 ∈ Cℋ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | atssch 29202 | . 2 ⊢ HAtoms ⊆ Cℋ | |
2 | 1 | sseli 3599 | 1 ⊢ (𝐴 ∈ HAtoms → 𝐴 ∈ Cℋ ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1990 Cℋ cch 27786 HAtomscat 27822 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-in 3581 df-ss 3588 df-at 29197 |
This theorem is referenced by: atsseq 29206 atcveq0 29207 chcv1 29214 chcv2 29215 hatomistici 29221 chrelati 29223 chrelat2i 29224 cvati 29225 cvexchlem 29227 cvp 29234 atnemeq0 29236 atcv0eq 29238 atcv1 29239 atexch 29240 atomli 29241 atoml2i 29242 atordi 29243 atcvatlem 29244 atcvati 29245 atcvat2i 29246 chirredlem1 29249 chirredlem2 29250 chirredlem3 29251 chirredlem4 29252 chirredi 29253 atcvat3i 29255 atcvat4i 29256 atdmd 29257 atmd 29258 atmd2 29259 atabsi 29260 mdsymlem2 29263 mdsymlem3 29264 mdsymlem5 29266 mdsymlem8 29269 atdmd2 29273 sumdmdi 29279 dmdbr4ati 29280 dmdbr5ati 29281 dmdbr6ati 29282 |
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