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Theorem fntopon 21252
Description: The class TopOn is a function with domain V. Analogue for topologies of fnmre 16733 for Moore collections. (Contributed by BJ, 29-Apr-2021.)
Assertion
Ref Expression
fntopon TopOn Fn V

Proof of Theorem fntopon
StepHypRef Expression
1 funtopon 21248 . 2 Fun TopOn
2 dmtopon 21251 . 2 dom TopOn = V
3 df-fn 6189 . 2 (TopOn Fn V ↔ (Fun TopOn ∧ dom TopOn = V))
41, 2, 3mpbir2an 699 1 TopOn Fn V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1508  Vcvv 3410  dom cdm 5404  Fun wfun 6180   Fn wfn 6181  TopOnctopon 21238
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929  ax-7 1966  ax-8 2053  ax-9 2060  ax-10 2080  ax-11 2094  ax-12 2107  ax-13 2302  ax-ext 2745  ax-sep 5057  ax-nul 5064  ax-pow 5116  ax-pr 5183
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 835  df-3an 1071  df-tru 1511  df-ex 1744  df-nf 1748  df-sb 2017  df-mo 2548  df-eu 2585  df-clab 2754  df-cleq 2766  df-clel 2841  df-nfc 2913  df-ral 3088  df-rab 3092  df-v 3412  df-dif 3827  df-un 3829  df-in 3831  df-ss 3838  df-nul 4174  df-if 4346  df-pw 4419  df-sn 4437  df-pr 4439  df-op 4443  df-uni 4710  df-br 4927  df-opab 4989  df-mpt 5006  df-id 5309  df-xp 5410  df-rel 5411  df-cnv 5412  df-co 5413  df-dm 5414  df-fun 6188  df-fn 6189  df-topon 21239
This theorem is referenced by:  toprntopon  21253
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