let p, q be Element of CQC-WFF ; :: thesis: p => (q => (p '&' q)) in TAUT
('not' (p '&' q)) => (('not' p) 'or' ('not' q)) in TAUT by Th17;
then A1: (p '&' q) 'or' (('not' p) 'or' ('not' q)) in TAUT by Lm1;
((p '&' q) 'or' (('not' p) 'or' ('not' q))) => (((p '&' q) 'or' ('not' p)) 'or' ('not' q)) in TAUT by Th27;
then A2: ((p '&' q) 'or' ('not' p)) 'or' ('not' q) in TAUT by A1, CQC_THE1:82;
(((p '&' q) 'or' ('not' p)) 'or' ('not' q)) => (('not' q) 'or' ((p '&' q) 'or' ('not' p))) in TAUT by Th8;
then ('not' q) 'or' ((p '&' q) 'or' ('not' p)) in TAUT by A2, CQC_THE1:82;
then A3: ('not' ('not' q)) => ((p '&' q) 'or' ('not' p)) in TAUT by Lm1;
q => ('not' ('not' q)) in TAUT by LUKASI_1:27;
then A4: q => ((p '&' q) 'or' ('not' p)) in TAUT by A3, LUKASI_1:3;
A5: q => (((p '&' q) 'or' ('not' p)) => (('not' p) 'or' (p '&' q))) in TAUT by Th8, LUKASI_1:13;
(q => (((p '&' q) 'or' ('not' p)) => (('not' p) 'or' (p '&' q)))) => ((q => ((p '&' q) 'or' ('not' p))) => (q => (('not' p) 'or' (p '&' q)))) in TAUT by LUKASI_1:11;
then (q => ((p '&' q) 'or' ('not' p))) => (q => (('not' p) 'or' (p '&' q))) in TAUT by A5, CQC_THE1:82;
then q => (('not' p) 'or' (p '&' q)) in TAUT by A4, CQC_THE1:82;
then q => (('not' ('not' p)) => (p '&' q)) in TAUT by Lm1;
then A6: ('not' ('not' p)) => (q => (p '&' q)) in TAUT by LUKASI_1:15;
p => ('not' ('not' p)) in TAUT by LUKASI_1:27;
hence p => (q => (p '&' q)) in TAUT by A6, LUKASI_1:3; :: thesis: verum