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 = ( CCfld |`s S )
Assertion cnfldsrngadd
|- ( S e. V -> + = ( +g ` R ) )

Proof

Step Hyp Ref Expression
1 cnfldsrngbas.r
 |-  R = ( CCfld |`s S )
2 cnfldadd
 |-  + = ( +g ` CCfld )
3 1 2 ressplusg
 |-  ( S e. V -> + = ( +g ` R ) )