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