let X be set ; :: thesis: for C, D being non empty set
for f being PartFunc of C,D st X misses dom f holds
f | X is constant
let C, D be non empty set ; :: thesis: for f being PartFunc of C,D st X misses dom f holds
f | X is constant
let f be PartFunc of C,D; :: thesis: ( X misses dom f implies f | X is constant )
assume A1: X /\ (dom f) = {} ; :: according to XBOOLE_0:def 7 :: thesis: f | X is constant

now :: thesis: ex d being Element of D st
for c being Element of C st c in X /\ (dom f) holds
f /. c = d

set d = the Element of D;
take d = the Element of D; :: thesis: for c being Element of C st c in X /\ (dom f) holds
f /. c = d
let c be Element of C; :: thesis: ( c in X /\ (dom f) implies f /. c = d )
thus ( c in X /\ (dom f) implies f /. c = d ) by A1; :: thesis: verum

end;

hence f | X is constant by Th35; :: thesis: verum