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Mirrors > Home > ILE Home > Th. List > 0ntop | 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 3428 | . 2 ⊢ ¬ ∅ ∈ ∅ | |
2 | 0opn 13667 | . 2 ⊢ (∅ ∈ Top → ∅ ∈ ∅) | |
3 | 1, 2 | mto 662 | 1 ⊢ ¬ ∅ ∈ Top |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 2148 ∅c0 3424 Topctop 13658 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4123 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2741 df-dif 3133 df-in 3137 df-ss 3144 df-nul 3425 df-pw 3579 df-sn 3600 df-uni 3812 df-top 13659 |
This theorem is referenced by: (None) |
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