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Theorem sn0top 22365
Description: The singleton of the empty set is a topology. (Contributed by Stefan Allan, 3-Mar-2006.) (Proof shortened by Mario Carneiro, 13-Aug-2015.)
Assertion
Ref Expression
sn0top {∅} ∈ Top

Proof of Theorem sn0top
StepHypRef Expression
1 sn0topon 22364 . 2 {∅} ∈ (TopOn‘∅)
21topontopi 22280 1 {∅} ∈ Top
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  c0 4283  {csn 4587  Topctop 22258
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5257  ax-nul 5264  ax-pow 5321  ax-pr 5385  ax-un 7673
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-pw 4563  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-opab 5169  df-mpt 5190  df-id 5532  df-xp 5640  df-rel 5641  df-cnv 5642  df-co 5643  df-dm 5644  df-iota 6449  df-fun 6499  df-fv 6505  df-top 22259  df-topon 22276
This theorem is referenced by:  restsn  22537  0cmp  22761  hmph0  23162  locfinref  32479  kur14  33867
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