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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > relfldext | Structured version Visualization version GIF version |
Description: The field extension is a relation. (Contributed by Thierry Arnoux, 29-Jul-2023.) |
Ref | Expression |
---|---|
relfldext | ⊢ Rel /FldExt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fldext 33670 | . 2 ⊢ /FldExt = {〈𝑒, 𝑓〉 ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒 ↾s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))} | |
2 | 1 | relopabiv 5833 | 1 ⊢ Rel /FldExt |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 395 = wceq 1537 ∈ wcel 2106 Rel wrel 5694 ‘cfv 6563 (class class class)co 7431 Basecbs 17245 ↾s cress 17274 SubRingcsubrg 20586 Fieldcfield 20747 /FldExtcfldext 33666 |
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 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-ss 3980 df-opab 5211 df-xp 5695 df-rel 5696 df-fldext 33670 |
This theorem is referenced by: extdgval 33682 |
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