let Al be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF Al
for f being FinSequence of CQC-WFF Al st |- f ^ <*p*> & |- f ^ <*('not' p)*> holds
|- f ^ <*q*>
let p, q be Element of CQC-WFF Al; :: thesis: for f being FinSequence of CQC-WFF Al st |- f ^ <*p*> & |- f ^ <*('not' p)*> holds
|- f ^ <*q*>
let f be FinSequence of CQC-WFF Al; :: thesis: ( |- f ^ <*p*> & |- f ^ <*('not' p)*> implies |- f ^ <*q*> )
A1: ( Ant (f ^ <*p*>) = f & Suc (f ^ <*p*>) = p ) by CALCUL_1:5;
assume ( |- f ^ <*p*> & |- f ^ <*('not' p)*> ) ; :: thesis: |- f ^ <*q*>
hence |- f ^ <*q*> by A1, CALCUL_1:44; :: thesis: verum