let X be Subset of CQC-WFF; :: thesis: for p, q, r being Element of CQC-WFF holds (p => q) => (('not' (q '&' r)) => ('not' (p '&' r))) in Cn X
let p, q, r be Element of CQC-WFF ; :: thesis: (p => q) => (('not' (q '&' r)) => ('not' (p '&' r))) in Cn X
for T being Subset of CQC-WFF st T is being_a_theory & X c= T holds
(p => q) => (('not' (q '&' r)) => ('not' (p '&' r))) in T by Def1;
hence (p => q) => (('not' (q '&' r)) => ('not' (p '&' r))) in Cn X by Def2; :: thesis: verum