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Mirrors > Home > MPE Home > Th. List > funtopon | Structured version Visualization version GIF version |
Description: The class TopOn is a function. (Contributed by BJ, 29-Apr-2021.) |
Ref | Expression |
---|---|
funtopon | ⊢ Fun TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-topon 21513 | . 2 ⊢ TopOn = (𝑦 ∈ V ↦ {𝑥 ∈ Top ∣ 𝑦 = ∪ 𝑥}) | |
2 | 1 | funmpt2 6389 | 1 ⊢ Fun TopOn |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 {crab 3142 Vcvv 3495 ∪ cuni 4832 Fun wfun 6344 Topctop 21495 TopOnctopon 21512 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 ax-sep 5196 ax-nul 5203 ax-pr 5322 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rab 3147 df-v 3497 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-if 4468 df-sn 4562 df-pr 4564 df-op 4568 df-br 5060 df-opab 5122 df-mpt 5140 df-id 5455 df-xp 5556 df-rel 5557 df-cnv 5558 df-co 5559 df-fun 6352 df-topon 21513 |
This theorem is referenced by: fntopon 21526 toprntopon 21527 |
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