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Mirrors > Home > MPE Home > Th. List > 0ntop | Structured version Visualization version GIF version |
Description: The empty set is not a topology. (Contributed by FL, 1-Jun-2008.) |
Ref | Expression |
---|---|
0ntop | ⊢ ¬ ∅ ∈ Top |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 4295 | . 2 ⊢ ¬ ∅ ∈ ∅ | |
2 | 0opn 21506 | . 2 ⊢ (∅ ∈ Top → ∅ ∈ ∅) | |
3 | 1, 2 | mto 199 | 1 ⊢ ¬ ∅ ∈ Top |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2110 ∅c0 4290 Topctop 21495 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-sep 5195 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3496 df-dif 3938 df-in 3942 df-ss 3951 df-nul 4291 df-pw 4540 df-sn 4561 df-uni 4832 df-top 21496 |
This theorem is referenced by: istps 21536 ordcmp 33790 onint1 33792 kelac1 39656 |
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