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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 31056 | . 2 ⊢ /FldExt = {〈𝑒, 𝑓〉 ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒 ↾s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))} | |
2 | 1 | relopabiv 5686 | 1 ⊢ Rel /FldExt |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 = wceq 1536 ∈ wcel 2113 Rel wrel 5553 ‘cfv 6348 (class class class)co 7149 Basecbs 16478 ↾s cress 16479 Fieldcfield 19498 SubRingcsubrg 19526 /FldExtcfldext 31052 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-v 3493 df-in 3936 df-ss 3945 df-opab 5122 df-xp 5554 df-rel 5555 df-fldext 31056 |
This theorem is referenced by: extdgval 31068 |
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