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 '&&' q)) => ((VAL g) . p) by LTLAXIO1:def 15
.= (((VAL g) . p) '&' ((VAL g) . q)) => ((VAL g) . p) by LTLAXIO1:31
.= 1 by A1 ; :: thesis: verum