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Theorem fntopon 21532
 Description: The class TopOn is a function with domain the universal class V. Analogue for topologies of fnmre 16857 for Moore collections. (Contributed by BJ, 29-Apr-2021.)
Assertion
Ref Expression
fntopon TopOn Fn V

Proof of Theorem fntopon
StepHypRef Expression
1 funtopon 21528 . 2 Fun TopOn
2 dmtopon 21531 . 2 dom TopOn = V
3 df-fn 6331 . 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 1538  Vcvv 3444  dom cdm 5523  Fun wfun 6322   Fn wfn 6323  TopOnctopon 21518 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-nul 5177  ax-pow 5234  ax-pr 5298 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ral 3114  df-rab 3118  df-v 3446  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-if 4429  df-pw 4502  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-opab 5096  df-mpt 5114  df-id 5428  df-xp 5529  df-rel 5530  df-cnv 5531  df-co 5532  df-dm 5533  df-fun 6330  df-fn 6331  df-topon 21519 This theorem is referenced by:  toprntopon  21533
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