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Theorem topnfn 15857
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 6554 . 2 ((TopSet‘𝑤) ↾t (Base‘𝑤)) ∈ V
2 df-topn 15855 . 2 TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
31, 2fnmpti 5920 1 TopOpen Fn V
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3172   Fn wfn 5784  cfv 5789  (class class class)co 6526  Basecbs 15643  TopSetcts 15722  t crest 15852  TopOpenctopn 15853
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4711  ax-pr 4827
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rex 2901  df-rab 2904  df-v 3174  df-sbc 3402  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-br 4578  df-opab 4638  df-mpt 4639  df-id 4942  df-xp 5033  df-rel 5034  df-cnv 5035  df-co 5036  df-dm 5037  df-iota 5753  df-fun 5791  df-fn 5792  df-fv 5797  df-ov 6529  df-topn 15855
This theorem is referenced by:  prdstopn  21188  prdstps  21189  xpstopnlem2  21371  prdstmdd  21684  prdstgpd  21685  prdsxmslem2  22091
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