| Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
||
| 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 33693 | . 2 ⊢ /FldExt = {〈𝑒, 𝑓〉 ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒 ↾s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))} | |
| 2 | 1 | relopabiv 5830 | 1 ⊢ Rel /FldExt |
| Colors of variables: wff setvar class |
| Syntax hints: ∧ wa 395 = wceq 1540 ∈ wcel 2108 Rel wrel 5690 ‘cfv 6561 (class class class)co 7431 Basecbs 17247 ↾s cress 17274 SubRingcsubrg 20569 Fieldcfield 20730 /FldExtcfldext 33689 |
| 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 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-ss 3968 df-opab 5206 df-xp 5691 df-rel 5692 df-fldext 33693 |
| This theorem is referenced by: extdgval 33705 |
| Copyright terms: Public domain | W3C validator |