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

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