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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 33146 | . 2 ⊢ Fne = {〈𝑥, 𝑦〉 ∣ (∪ 𝑥 = ∪ 𝑦 ∧ ∀𝑧 ∈ 𝑥 𝑧 ⊆ ∪ (𝑦 ∩ 𝒫 𝑧))} | |
2 | 1 | relopabi 5537 | 1 ⊢ Rel Fne |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 387 = wceq 1507 ∀wral 3082 ∩ cin 3824 ⊆ wss 3825 𝒫 cpw 4416 ∪ cuni 4706 Rel wrel 5405 Fnecfne 33145 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1964 ax-8 2050 ax-9 2057 ax-10 2077 ax-11 2091 ax-12 2104 ax-ext 2745 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-3an 1070 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2014 df-clab 2754 df-cleq 2765 df-clel 2840 df-nfc 2912 df-rab 3091 df-v 3411 df-dif 3828 df-un 3830 df-in 3832 df-ss 3839 df-nul 4174 df-if 4345 df-sn 4436 df-pr 4438 df-op 4442 df-opab 4986 df-xp 5406 df-rel 5407 df-fne 33146 |
This theorem is referenced by: isfne 33148 isfne4 33149 fnetr 33160 fneval 33161 fneer 33162 fnessref 33166 |
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