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