Metamath Proof Explorer

Theorem replusg

Description: The addition operation of the field of reals. (Contributed by Thierry Arnoux, 21-Jan-2018)

Ref Expression
Assertion replusg 
|- + = ( +g ` RRfld )

Proof

Step Hyp Ref Expression
1 reex 
 |-  RR e. _V
2 df-refld 
 |-  RRfld = ( CCfld |`s RR )
3 cnfldadd 
 |-  + = ( +g ` CCfld )
4 2 3 ressplusg 
 |-  ( RR e. _V -> + = ( +g ` RRfld ) )
5 1 4 ax-mp 
 |-  + = ( +g ` RRfld )