let p, q be Element of LTLB_WFF ; :: thesis: ('not' (p => q)) => ('not' q) is ctaut
let g be Function of LTLB_WFF,BOOLEAN; :: according to LTLAXIO1:def 16 :: thesis: (VAL g) . (('not' (p => q)) => ('not' q)) = 1
set v = VAL g;
A1: (VAL g) . TFALSUM = 0 by LTLAXIO1:def 15;
A2: ( (VAL g) . q = 1 or (VAL g) . q = 0 ) by XBOOLEAN:def 3;
thus (VAL g) . (('not' (p => q)) => ('not' q)) = ((VAL g) . ('not' (p => q))) => ((VAL g) . ('not' q)) by LTLAXIO1:def 15
.= (((VAL g) . (p => q)) => ((VAL g) . TFALSUM)) => ((VAL g) . ('not' q)) by LTLAXIO1:def 15
.= ((((VAL g) . p) => ((VAL g) . q)) => ((VAL g) . TFALSUM)) => ((VAL g) . ('not' q)) by LTLAXIO1:def 15
.= ((((VAL g) . p) => ((VAL g) . q)) => ((VAL g) . TFALSUM)) => (((VAL g) . q) => ((VAL g) . TFALSUM)) by LTLAXIO1:def 15
.= 1 by A2, A1 ; :: thesis: verum