let X be set ; :: thesis: ( X is real-membered implies X is complex-membered )
assume A5: X is real-membered ; :: thesis: X is complex-membered
let x be object ; :: according to MEMBERED:def 1 :: thesis: ( x in X implies x is complex )
assume x in X ; :: thesis: x is complex
then x is real by A5;
then x in REAL ;
hence x in COMPLEX by NUMBERS:11; :: according to XCMPLX_0:def 2 :: thesis: verum