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Mirrors > Home > MPE Home > Th. List > Mathboxes > onsstopbas | Structured version Visualization version GIF version |
Description: The class of ordinal numbers is a subclass of the class of topological bases. (Contributed by Chen-Pang He, 8-Oct-2015.) |
Ref | Expression |
---|---|
onsstopbas | ⊢ On ⊆ TopBases |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ontopbas 33293 | . 2 ⊢ (𝑥 ∈ On → 𝑥 ∈ TopBases) | |
2 | 1 | ssriv 3863 | 1 ⊢ On ⊆ TopBases |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3830 Oncon0 6029 TopBasesctb 21257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-13 2301 ax-ext 2751 ax-sep 5060 ax-nul 5067 ax-pr 5186 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-3or 1069 df-3an 1070 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-mo 2547 df-eu 2584 df-clab 2760 df-cleq 2772 df-clel 2847 df-nfc 2919 df-ne 2969 df-ral 3094 df-rex 3095 df-rab 3098 df-v 3418 df-sbc 3683 df-dif 3833 df-un 3835 df-in 3837 df-ss 3844 df-pss 3846 df-nul 4180 df-if 4351 df-pw 4424 df-sn 4442 df-pr 4444 df-op 4448 df-uni 4713 df-br 4930 df-opab 4992 df-tr 5031 df-eprel 5317 df-po 5326 df-so 5327 df-fr 5366 df-we 5368 df-ord 6032 df-on 6033 df-bases 21258 |
This theorem is referenced by: onpsstopbas 33295 |
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