Metamath Proof Explorer


Definition df-frac

Description: Define the field of fractions of a given integral domain. (Contributed by Thierry Arnoux, 26-Apr-2025)

Ref Expression
Assertion df-frac ⊢ Frac = r ∈ V ⟼ r RLocal RLReg ⁡ r

Detailed syntax breakdown

Step Hyp Ref Expression
0 cfrac class Frac
1 vr setvar r
2 cvv class V
3 1 cv setvar r
4 crloc class RLocal
5 crlreg class RLReg
6 3 5 cfv class RLReg ⁡ r
7 3 6 4 co class r RLocal RLReg ⁡ r
8 1 2 7 cmpt class r ∈ V ⟼ r RLocal RLReg ⁡ r
9 0 8 wceq wff Frac = r ∈ V ⟼ r RLocal RLReg ⁡ r