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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 36339 | . 2 ⊢ Fne = {〈𝑥, 𝑦〉 ∣ (∪ 𝑥 = ∪ 𝑦 ∧ ∀𝑧 ∈ 𝑥 𝑧 ⊆ ∪ (𝑦 ∩ 𝒫 𝑧))} | |
| 2 | 1 | relopabiv 5829 | 1 ⊢ Rel Fne | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∧ wa 395 = wceq 1539 ∀wral 3060 ∩ cin 3949 ⊆ wss 3950 𝒫 cpw 4599 ∪ cuni 4906 Rel wrel 5689 Fnecfne 36338 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1542 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-ss 3967 df-opab 5205 df-xp 5690 df-rel 5691 df-fne 36339 | 
| This theorem is referenced by: isfne 36341 isfne4 36342 fnetr 36353 fneval 36354 fneer 36355 fnessref 36359 | 
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