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Mirrors > Home > HSE Home > Th. List > atssch | Structured version Visualization version GIF version |
Description: Atoms are a subset of the Hilbert lattice. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.) |
Ref | Expression |
---|---|
atssch | ⊢ HAtoms ⊆ Cℋ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-at 30115 | . 2 ⊢ HAtoms = {𝑥 ∈ Cℋ ∣ 0ℋ ⋖ℋ 𝑥} | |
2 | 1 | ssrab3 4057 | 1 ⊢ HAtoms ⊆ Cℋ |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3936 class class class wbr 5066 Cℋ cch 28706 0ℋc0h 28712 ⋖ℋ ccv 28741 HAtomscat 28742 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-in 3943 df-ss 3952 df-at 30115 |
This theorem is referenced by: atelch 30121 shatomistici 30138 hatomistici 30139 chpssati 30140 |
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