reconsider e = RealFuncUnit A as Element of (RRing A) ;
take e ; :: according to GROUP_1:def 1 :: thesis: for b₁ being Element of the carrier of (RRing A) holds
( b₁ * e = b₁ & e * b₁ = b₁ )
thus for b₁ being Element of the carrier of (RRing A) holds
( b₁ * e = b₁ & e * b₁ = b₁ ) by Lm3; :: thesis: verum