let X be set ; :: thesis: ( X is real-membered implies X is ext-real-membered )
assume A4: X is real-membered ; :: thesis: X is ext-real-membered
let x be object ; :: according to MEMBERED:def 2 :: thesis: ( x in X implies x is ext-real )
assume x in X ; :: thesis: x is ext-real
then x is real by A4;
then x in REAL ;
hence x in ExtREAL by NUMBERS:31; :: according to XXREAL_0:def 1 :: thesis: verum