let X be set ; :: thesis: ( X is rational-functions-membered implies X is real-functions-membered )
assume A3: for x being set st x in X holds
x is rational-valued Function ; :: according to VALUED_2:def 5 :: thesis: X is real-functions-membered
let x be set ; :: according to VALUED_2:def 4 :: thesis: ( x in X implies x is real-valued Function )
thus ( x in X implies x is real-valued Function ) by A3; :: thesis: verum