let V, C be non empty set ; ex f being Element of PFuncs (V,C) st f <> {}
consider a being object such that
A1:
a in V
by XBOOLE_0:def 1;
consider b being object such that
A2:
b in C
by XBOOLE_0:def 1;
set f = {[a,b]};
{a} c= V
by A1, ZFMISC_1:31;
then A3:
dom {[a,b]} c= V
by RELAT_1:9;
{b} c= C
by A2, ZFMISC_1:31;
then
rng {[a,b]} c= C
by RELAT_1:9;
then reconsider f = {[a,b]} as Element of PFuncs (V,C) by A3, PARTFUN1:def 3;
f <> {}
;
hence
ex f being Element of PFuncs (V,C) st f <> {}
; verum