let X be Subset of MC-wff ; :: thesis: for p, q being Element of MC-wff st p in CnS4 X & p => q in CnS4 X holds
q in CnS4 X
let p, q be Element of MC-wff ; :: thesis: ( p in CnS4 X & p => q in CnS4 X implies q in CnS4 X )
assume A1: ( p in CnS4 X & p => q in CnS4 X ) ; :: thesis: q in CnS4 X
for T being Subset of MC-wff st T is S4_theory & X c= T holds
q in T

proof

let T be Subset of MC-wff ; :: thesis: ( T is S4_theory & X c= T implies q in T )
assume A2: ( T is S4_theory & X c= T ) ; :: thesis: q in T
then ( p in T & p => q in T ) by A1, Def23;
hence q in T by A2, Def22; :: thesis: verum

end;

hence q in CnS4 X by Def23; :: thesis: verum