let p, q be Element of CQC-WFF ; :: thesis: ( (p => ('not' ('not' q))) => (p => q) in TAUT & (p => q) => (p => ('not' ('not' q))) in TAUT )
('not' ('not' q)) => q in TAUT by Th25;
then ( (p => (('not' ('not' q)) => q)) => ((p => ('not' ('not' q))) => (p => q)) in TAUT & p => (('not' ('not' q)) => q) in TAUT ) by Th11, Th13;
hence (p => ('not' ('not' q))) => (p => q) in TAUT by CQC_THE1:82; :: thesis: (p => q) => (p => ('not' ('not' q))) in TAUT
q => ('not' ('not' q)) in TAUT by Th27;
then ( (p => (q => ('not' ('not' q)))) => ((p => q) => (p => ('not' ('not' q)))) in TAUT & p => (q => ('not' ('not' q))) in TAUT ) by Th11, Th13;
hence (p => q) => (p => ('not' ('not' q))) in TAUT by CQC_THE1:82; :: thesis: verum