let p, q be Element of HP-WFF ; :: thesis: p => q <> VERUM
p => q = <*1*> ^ (p ^ q) by FINSEQ_1:45;
then ( (p => q) . 1 = 1 & VERUM . 1 = 0 ) by FINSEQ_1:57, FINSEQ_1:58;
hence p => q <> VERUM ; :: thesis: verum