let X be Subset of MC-wff; :: thesis: for p, q being Element of MC-wff holds (Nes (p => q)) => ((Nes p) => (Nes q)) in CnS4 X
let p, q be Element of MC-wff ; :: thesis: (Nes (p => q)) => ((Nes p) => (Nes q)) in CnS4 X
for T being Subset of MC-wff st T is S4_theory & X c= T holds
(Nes (p => q)) => ((Nes p) => (Nes q)) in T ;
hence (Nes (p => q)) => ((Nes p) => (Nes q)) in CnS4 X by Def23; :: thesis: verum