set M = the carrier of L;
for u being set st u in the carrier of L holds
u in the carrier of L ;
then reconsider M = the carrier of L as Subset of L by TARSKI:def 3;
reconsider M = M as non empty Subset of L ;
take M ; :: thesis: M is left-ideal
for p, x being Element of L st x in M holds
p * x in M ;
hence M is left-ideal by Def2; :: thesis: verum