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Theorem fntopon 22825
Description: The class TopOn is a function with domain the universal class V. Analogue for topologies of fnmre 17570 for Moore collections. (Contributed by BJ, 29-Apr-2021.)
Assertion
Ref Expression
fntopon TopOn Fn V

Proof of Theorem fntopon
StepHypRef Expression
1 funtopon 22821 . 2 Fun TopOn
2 dmtopon 22824 . 2 dom TopOn = V
3 df-fn 6551 . 2 (TopOn Fn V ↔ (Fun TopOn ∧ dom TopOn = V))
41, 2, 3mpbir2an 710 1 TopOn Fn V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  Vcvv 3471  dom cdm 5678  Fun wfun 6542   Fn wfn 6543  TopOnctopon 22811
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pow 5365  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2530  df-eu 2559  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-pw 4605  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4909  df-br 5149  df-opab 5211  df-mpt 5232  df-id 5576  df-xp 5684  df-rel 5685  df-cnv 5686  df-co 5687  df-dm 5688  df-fun 6550  df-fn 6551  df-topon 22812
This theorem is referenced by:  toprntopon  22826
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