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Mirrors > Home > MPE Home > Th. List > Mathboxes > isofld | Structured version Visualization version Unicode version |
Description: An ordered field is a field with a total ordering compatible with its operations. (Contributed by Thierry Arnoux, 23-Mar-2018.) |
Ref | Expression |
---|---|
isofld | oField Field oRing |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ofld 29798 | . 2 oField Field oRing | |
2 | 1 | elin2 3801 | 1 oField Field oRing |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wcel 1990 Fieldcfield 18748 oRingcorng 29795 oFieldcofld 29796 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ofld 29798 |
This theorem is referenced by: ofldfld 29810 ofldtos 29811 ofldlt1 29813 ofldchr 29814 subofld 29816 isarchiofld 29817 reofld 29840 nn0omnd 29841 |
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