let R be Relation; :: thesis: ( R is rational-functions-valued implies R is real-functions-valued )
assume A3: rng R is rational-functions-membered ; :: according to VALUED_2:def 23 :: thesis: R is real-functions-valued
let y be set ; :: according to VALUED_2:def 4,VALUED_2:def 22 :: thesis: ( y in rng R implies y is real-valued Function )
thus ( y in rng R implies y is real-valued Function ) by A3; :: thesis: verum