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Theorem fntopon 22770
Description: The class TopOn is a function with domain the universal class V. Analogue for topologies of fnmre 17540 for Moore collections. (Contributed by BJ, 29-Apr-2021.)
Assertion
Ref Expression
fntopon TopOn Fn V

Proof of Theorem fntopon
StepHypRef Expression
1 funtopon 22766 . 2 Fun TopOn
2 dmtopon 22769 . 2 dom TopOn = V
3 df-fn 6537 . 2 (TopOn Fn V ↔ (Fun TopOn ∧ dom TopOn = V))
41, 2, 3mpbir2an 708 1 TopOn Fn V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  Vcvv 3466  dom cdm 5667  Fun wfun 6528   Fn wfn 6529  TopOnctopon 22756
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pow 5354  ax-pr 5418
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2526  df-eu 2555  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-pw 4597  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-opab 5202  df-mpt 5223  df-id 5565  df-xp 5673  df-rel 5674  df-cnv 5675  df-co 5676  df-dm 5677  df-fun 6536  df-fn 6537  df-topon 22757
This theorem is referenced by:  toprntopon  22771
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