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Theorem bj-funtopon 32719
 Description: TopOn is a function. (Contributed by BJ, 29-Apr-2021.)
Assertion
Ref Expression
bj-funtopon Fun TopOn

Proof of Theorem bj-funtopon
Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-topon 20644 . 2 TopOn = (𝑦 ∈ V ↦ {𝑥 ∈ Top ∣ 𝑦 = 𝑥})
21funmpt2 5890 1 Fun TopOn
 Colors of variables: wff setvar class Syntax hints:   = wceq 1480  {crab 2911  Vcvv 3189  ∪ cuni 4407  Fun wfun 5846  Topctop 20626  TopOnctopon 20643 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4746  ax-nul 4754  ax-pr 4872 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rab 2916  df-v 3191  df-dif 3562  df-un 3564  df-in 3566  df-ss 3573  df-nul 3897  df-if 4064  df-sn 4154  df-pr 4156  df-op 4160  df-br 4619  df-opab 4679  df-mpt 4680  df-id 4994  df-xp 5085  df-rel 5086  df-cnv 5087  df-co 5088  df-fun 5854  df-topon 20644 This theorem is referenced by:  bj-fntopon  32726  bj-toprntopon  32727
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