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 ⊢ Frac
1 vr ⊢ 𝑟
2 cvv ⊢ V
3 1 cv ⊢ 𝑟
4 crloc ⊢ RLocal
5 crlreg ⊢ RLReg
6 3 5 cfv ⊢ ( RLReg ‘ 𝑟 )
7 3 6 4 co ⊢ ( 𝑟 RLocal ( RLReg ‘ 𝑟 ) )
8 1 2 7 cmpt ⊢ ( 𝑟 ∈ V ↦ ( 𝑟 RLocal ( RLReg ‘ 𝑟 ) ) )
9 0 8 wceq ⊢ Frac = ( 𝑟 ∈ V ↦ ( 𝑟 RLocal ( RLReg ‘ 𝑟 ) ) )