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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 35160 | . 2 ⊢ Fne = {〈𝑥, 𝑦〉 ∣ (∪ 𝑥 = ∪ 𝑦 ∧ ∀𝑧 ∈ 𝑥 𝑧 ⊆ ∪ (𝑦 ∩ 𝒫 𝑧))} | |
2 | 1 | relopabiv 5818 | 1 ⊢ Rel Fne |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 397 = wceq 1542 ∀wral 3062 ∩ cin 3946 ⊆ wss 3947 𝒫 cpw 4601 ∪ cuni 4907 Rel wrel 5680 Fnecfne 35159 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3477 df-in 3954 df-ss 3964 df-opab 5210 df-xp 5681 df-rel 5682 df-fne 35160 |
This theorem is referenced by: isfne 35162 isfne4 35163 fnetr 35174 fneval 35175 fneer 35176 fnessref 35180 |
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