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Theorem singempcon 25604
Description: The singleton of the empty set is a connected topology. (Contributed by FL, 22-Dec-2008.) (Revised by Mario Carneiro, 11-Nov-2013.)
Assertion
Ref Expression
singempcon  |-  { (/) }  e.  Con

Proof of Theorem singempcon
StepHypRef Expression
1 dfsn2 3656 . 2  |-  { (/) }  =  { (/) ,  (/) }
2 indiscon 17146 . 2  |-  { (/) ,  (/) }  e.  Con
31, 2eqeltri 2355 1  |-  { (/) }  e.  Con
Colors of variables: wff set class
Syntax hints:    e. wcel 1686   (/)c0 3457   {csn 3642   {cpr 3643   Conccon 17139
This theorem is referenced by:  intvconlem1  25714
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-13 1688  ax-14 1690  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-sep 4143  ax-nul 4151  ax-pow 4190  ax-pr 4216  ax-un 4514
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-eu 2149  df-mo 2150  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ne 2450  df-ral 2550  df-rex 2551  df-rab 2554  df-v 2792  df-sbc 2994  df-dif 3157  df-un 3159  df-in 3161  df-ss 3168  df-nul 3458  df-if 3568  df-pw 3629  df-sn 3648  df-pr 3649  df-op 3651  df-uni 3830  df-br 4026  df-opab 4080  df-mpt 4081  df-id 4311  df-xp 4697  df-rel 4698  df-cnv 4699  df-co 4700  df-dm 4701  df-iota 5221  df-fun 5259  df-fv 5265  df-top 16638  df-topon 16641  df-cld 16758  df-con 17140
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