let p, q be Element of LTLB_WFF ; :: thesis: p => (q => p) is ctaut
let g be Function of LTLB_WFF,BOOLEAN; :: according to LTLAXIO1:def 16 :: thesis: (VAL g) . (p => (q => p)) = 1
set v = VAL g;
A1: ( (VAL g) . p = 1 or (VAL g) . p = 0 ) by XBOOLEAN:def 3;
thus (VAL g) . (p => (q => p)) = ((VAL g) . p) => ((VAL g) . (q => p)) by LTLAXIO1:def 15
.= ((VAL g) . p) => (((VAL g) . q) => ((VAL g) . p)) by LTLAXIO1:def 15
.= 1 by A1 ; :: thesis: verum