let p, q, s be Element of HP-WFF ; :: thesis: ((p => q) '&' (p => s)) => (p => (q '&' s)) in HP_TAUT
set P = p => q;
set Q = p => s;
set S = p => (q '&' s);
A1: (p => q) => ((p => s) => (p => (q '&' s))) in HP_TAUT by Th35;
((p => q) => ((p => s) => (p => (q '&' s)))) => (((p => q) '&' (p => s)) => (p => (q '&' s))) in HP_TAUT by Th34;
hence ((p => q) '&' (p => s)) => (p => (q '&' s)) in HP_TAUT by A1, Def10; :: thesis: verum