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Theorem topnfn 16698
Description: The topology extractor function is a function on the universe. (Contributed by Mario Carneiro, 13-Aug-2015.)
Assertion
Ref Expression
topnfn TopOpen Fn V

Proof of Theorem topnfn
StepHypRef Expression
1 ovex 7188 . 2 ((TopSet‘𝑤) ↾t (Base‘𝑤)) ∈ V
2 df-topn 16696 . 2 TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
31, 2fnmpti 6490 1 TopOpen Fn V
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3494   Fn wfn 6349  cfv 6354  (class class class)co 7155  Basecbs 16482  TopSetcts 16570  t crest 16693  TopOpenctopn 16694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793  ax-sep 5202  ax-nul 5209  ax-pr 5329
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-mo 2618  df-eu 2650  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ral 3143  df-rex 3144  df-rab 3147  df-v 3496  df-sbc 3772  df-dif 3938  df-un 3940  df-in 3942  df-ss 3951  df-nul 4291  df-if 4467  df-sn 4567  df-pr 4569  df-op 4573  df-uni 4838  df-br 5066  df-opab 5128  df-mpt 5146  df-id 5459  df-xp 5560  df-rel 5561  df-cnv 5562  df-co 5563  df-dm 5564  df-iota 6313  df-fun 6356  df-fn 6357  df-fv 6362  df-ov 7158  df-topn 16696
This theorem is referenced by:  prdstopn  22235  prdstps  22236  xpstopnlem2  22418  prdstmdd  22731  prdstgpd  22732  prdsxmslem2  23138
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