let X be set ; :: thesis: ( X is real-functions-membered implies X is complex-functions-membered )
assume A4: for x being set st x in X holds
x is real-valued Function ; :: according to VALUED_2:def 4 :: thesis: X is complex-functions-membered
let x be set ; :: according to VALUED_2:def 2 :: thesis: ( x in X implies x is complex-valued Function )
thus ( x in X implies x is complex-valued Function ) by A4; :: thesis: verum