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Theorem llytop 20471
 Description: A locally space is a topological space. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
llytop Locally

Proof of Theorem llytop
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 islly 20467 . 2 Locally t
21simplbi 461 1 Locally
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wcel 1868  wral 2775  wrex 2776   cin 3435  cpw 3979  (class class class)co 6301   ↾t crest 15304  ctop 19901  Locally clly 20463 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-rex 2781  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3910  df-sn 3997  df-pr 3999  df-op 4003  df-uni 4217  df-br 4421  df-iota 5561  df-fv 5605  df-ov 6304  df-lly 20465 This theorem is referenced by:  llynlly  20476  islly2  20483  llyrest  20484  llyidm  20487  nllyidm  20488  toplly  20489  lly1stc  20495  txlly  20635
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