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Mirrors > Home > MPE Home > Th. List > Mathboxes > fnerel | Structured version Visualization version GIF version |
Description: Fineness is a relation. (Contributed by Jeff Hankins, 28-Sep-2009.) |
Ref | Expression |
---|---|
fnerel | ⊢ Rel Fne |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fne 32669 | . 2 ⊢ Fne = {〈𝑥, 𝑦〉 ∣ (∪ 𝑥 = ∪ 𝑦 ∧ ∀𝑧 ∈ 𝑥 𝑧 ⊆ ∪ (𝑦 ∩ 𝒫 𝑧))} | |
2 | 1 | relopabi 5383 | 1 ⊢ Rel Fne |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 382 = wceq 1631 ∀wral 3061 ∩ cin 3722 ⊆ wss 3723 𝒫 cpw 4298 ∪ cuni 4575 Rel wrel 5255 Fnecfne 32668 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 df-3an 1073 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-rab 3070 df-v 3353 df-dif 3726 df-un 3728 df-in 3730 df-ss 3737 df-nul 4064 df-if 4227 df-sn 4318 df-pr 4320 df-op 4324 df-opab 4848 df-xp 5256 df-rel 5257 df-fne 32669 |
This theorem is referenced by: isfne 32671 isfne4 32672 fnetr 32683 fneval 32684 fneer 32685 fnessref 32689 |
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