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Mirrors > Home > MPE Home > Th. List > fntopon | Structured version Visualization version GIF version |
Description: The class TopOn is a function with domain V. Analogue for topologies of fnmre 16733 for Moore collections. (Contributed by BJ, 29-Apr-2021.) |
Ref | Expression |
---|---|
fntopon | ⊢ TopOn Fn V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funtopon 21248 | . 2 ⊢ Fun TopOn | |
2 | dmtopon 21251 | . 2 ⊢ dom TopOn = V | |
3 | df-fn 6189 | . 2 ⊢ (TopOn Fn V ↔ (Fun TopOn ∧ dom TopOn = V)) | |
4 | 1, 2, 3 | mpbir2an 699 | 1 ⊢ TopOn Fn V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1508 Vcvv 3410 dom cdm 5404 Fun wfun 6180 Fn wfn 6181 TopOnctopon 21238 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1759 ax-4 1773 ax-5 1870 ax-6 1929 ax-7 1966 ax-8 2053 ax-9 2060 ax-10 2080 ax-11 2094 ax-12 2107 ax-13 2302 ax-ext 2745 ax-sep 5057 ax-nul 5064 ax-pow 5116 ax-pr 5183 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 835 df-3an 1071 df-tru 1511 df-ex 1744 df-nf 1748 df-sb 2017 df-mo 2548 df-eu 2585 df-clab 2754 df-cleq 2766 df-clel 2841 df-nfc 2913 df-ral 3088 df-rab 3092 df-v 3412 df-dif 3827 df-un 3829 df-in 3831 df-ss 3838 df-nul 4174 df-if 4346 df-pw 4419 df-sn 4437 df-pr 4439 df-op 4443 df-uni 4710 df-br 4927 df-opab 4989 df-mpt 5006 df-id 5309 df-xp 5410 df-rel 5411 df-cnv 5412 df-co 5413 df-dm 5414 df-fun 6188 df-fn 6189 df-topon 21239 |
This theorem is referenced by: toprntopon 21253 |
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