Metamath Proof Explorer


Theorem cnfldsrngadd

Description: The group addition operation of a subring of the field of complex numbers. (Contributed by AV, 31-Jan-2020)

Ref Expression
Hypothesis cnfldsrngbas.r ⊢ 𝑅 = ( ℂfld ↾s 𝑆 )
Assertion cnfldsrngadd ( 𝑆 ∈ 𝑉 → + = ( +g ‘ 𝑅 ) )

Proof

Step Hyp Ref Expression
1 cnfldsrngbas.r ⊢ 𝑅 = ( ℂfld ↾s 𝑆 )
2 cnfldadd ⊢ + = ( +g ‘ ℂfld )
3 1 2 ressplusg ⊢ ( 𝑆 ∈ 𝑉 → + = ( +g ‘ 𝑅 ) )