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Theorem topnfn 13346
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 5899 . 2  |-  ( (TopSet `  w )t  ( Base `  w
) )  e.  _V
2 df-topn 13344 . 2  |-  TopOpen  =  ( w  e.  _V  |->  ( (TopSet `  w )t  ( Base `  w ) ) )
31, 2fnmpti 5388 1  |-  TopOpen  Fn  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2801    Fn wfn 5266   ` cfv 5271  (class class class)co 5874   Basecbs 13164  TopSetcts 13230   ↾t crest 13341   TopOpenctopn 13342
This theorem is referenced by:  prdstopn  17338  prdstps  17339  xpstopnlem2  17518  prdstmdd  17822  prdstgpd  17823  prdsxmslem2  18091
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-iota 5235  df-fun 5273  df-fn 5274  df-fv 5279  df-ov 5877  df-topn 13344
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