let p, q, s be Element of MC-wff ; :: thesis: ((p '&' s) => q) => ((p '&' s) => (q '&' s)) in IPC-Taut
set P = p '&' s;
A1: ((p '&' s) => q) => (((p '&' s) => s) => ((p '&' s) => (q '&' s))) in IPC-Taut by Th38;
(p '&' s) => s in IPC-Taut by Def14;
hence ((p '&' s) => q) => ((p '&' s) => (q '&' s)) in IPC-Taut by A1, Th32; :: thesis: verum