Theorem funtopon 22926

Description: The class TopOn is a function. (Contributed by BJ, 29-Apr-2021.)

Assertion

Ref	Expression
funtopon	⊢ Fun TopOn

Proof of Theorem funtopon

Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-topon 22917	. 2 ⊢ TopOn = (𝑦 ∈ V ↦ {𝑥 ∈ Top ∣ 𝑦 = ∪ 𝑥})
2	1	funmpt2 6605	1 ⊢ Fun TopOn

Syntax hints:   = wceq 1540  {crab 3436  Vcvv 3480  ∪ cuni 4907  Fun wfun 6555  Topctop 22899  TopOnctopon 22916

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-opab 5206  df-mpt 5226  df-id 5578  df-xp 5691  df-rel 5692  df-cnv 5693  df-co 5694  df-fun 6563  df-topon 22917

This theorem is referenced by:  fntopon  22930  toprntopon  22931