let R be Relation; :: thesis: ( R is real-functions-valued implies R is complex-functions-valued )
assume A5: rng R is real-functions-membered ; :: according to VALUED_2:def 22 :: thesis: R is complex-functions-valued
let y be set ; :: according to VALUED_2:def 2,VALUED_2:def 20 :: thesis: ( y in rng R implies y is complex-valued Function )
thus ( y in rng R implies y is complex-valued Function ) by A5; :: thesis: verum