let X be Subset of MC-wff ; :: thesis: for p, q being Element of MC-wff st p in CnCPC X & p => q in CnCPC X holds
q in CnCPC X
let p, q be Element of MC-wff ; :: thesis: ( p in CnCPC X & p => q in CnCPC X implies q in CnCPC X )
assume A1: ( p in CnCPC X & p => q in CnCPC X ) ; :: thesis: q in CnCPC X
for T being Subset of MC-wff st T is CPC_theory & X c= T holds
q in T

proof

let T be Subset of MC-wff ; :: thesis: ( T is CPC_theory & X c= T implies q in T )
assume A2: ( T is CPC_theory & X c= T ) ; :: thesis: q in T
then ( p in T & p => q in T ) by A1, Def20;
hence q in T by A2, Def19; :: thesis: verum

end;

hence q in CnCPC X by Def20; :: thesis: verum