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Mirrors > Home > MPE Home > Th. List > df-ur | Structured version Visualization version GIF version |
Description: Define the multiplicative neutral element of a ring. This definition works by extracting the 0g element, i.e. the neutral element in a group or monoid, and transferring it to the multiplicative monoid via the mulGrp function (df-mgp 18313). See also dfur2 18327, which derives the "traditional" definition as the unique element of a ring which is left- and right-neutral under multiplication. (Contributed by NM, 27-Aug-2011.) (Revised by Mario Carneiro, 27-Dec-2014.) |
Ref | Expression |
---|---|
df-ur | ⊢ 1r = (0g ∘ mulGrp) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cur 18324 | . 2 class 1r | |
2 | c0g 15923 | . . 3 class 0g | |
3 | cmgp 18312 | . . 3 class mulGrp | |
4 | 2, 3 | ccom 5042 | . 2 class (0g ∘ mulGrp) |
5 | 1, 4 | wceq 1475 | 1 wff 1r = (0g ∘ mulGrp) |
Colors of variables: wff setvar class |
This definition is referenced by: ringidval 18326 prds1 18437 pws1 18439 |
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