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Theorem fntopon 20776
Description: The class TopOn is a function with domain V. Analogue for topologies of fnmre 16298 for Moore collections. (Contributed by BJ, 29-Apr-2021.)
Assertion
Ref Expression
fntopon TopOn Fn V

Proof of Theorem fntopon
StepHypRef Expression
1 funtopon 20773 . 2 Fun TopOn
2 dmtopon 20775 . 2 dom TopOn = V
3 df-fn 5929 . 2 (TopOn Fn V ↔ (Fun TopOn ∧ dom TopOn = V))
41, 2, 3mpbir2an 975 1 TopOn Fn V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  Vcvv 3231  dom cdm 5143  Fun wfun 5920   Fn wfn 5921  TopOnctopon 20763
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pow 4873  ax-pr 4936
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-pw 4193  df-sn 4211  df-pr 4213  df-op 4217  df-uni 4469  df-br 4686  df-opab 4746  df-mpt 4763  df-id 5053  df-xp 5149  df-rel 5150  df-cnv 5151  df-co 5152  df-dm 5153  df-fun 5928  df-fn 5929  df-topon 20764
This theorem is referenced by:  toprntopon  20777
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