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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 4242 | . 2 ⊢ ¬ ∅ ∈ ∅ | |
2 | 0opn 21798 | . 2 ⊢ (∅ ∈ Top → ∅ ∈ ∅) | |
3 | 1, 2 | mto 200 | 1 ⊢ ¬ ∅ ∈ Top |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2110 ∅c0 4234 Topctop 21787 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-11 2158 ax-ext 2708 ax-sep 5189 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-ral 3063 df-rex 3064 df-rab 3067 df-v 3407 df-dif 3866 df-in 3870 df-ss 3880 df-nul 4235 df-pw 4512 df-sn 4539 df-uni 4817 df-top 21788 |
This theorem is referenced by: istps 21828 ordcmp 34370 onint1 34372 kelac1 40589 |
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