Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-flddrng | Structured version Visualization version GIF version |
Description: Fields are division rings. (Contributed by BJ, 6-Jan-2024.) |
Ref | Expression |
---|---|
bj-flddrng | ⊢ Field ⊆ DivRing |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-field 19770 | . 2 ⊢ Field = (DivRing ∩ CRing) | |
2 | inss1 4143 | . 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing | |
3 | 1, 2 | eqsstri 3935 | 1 ⊢ Field ⊆ DivRing |
Colors of variables: wff setvar class |
Syntax hints: ∩ cin 3865 ⊆ wss 3866 CRingccrg 19563 DivRingcdr 19767 Fieldcfield 19768 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3410 df-in 3873 df-ss 3883 df-field 19770 |
This theorem is referenced by: bj-rrdrg 35195 |
Copyright terms: Public domain | W3C validator |