let A be non empty set ; :: thesis: for J being interpretation of A
for v being Element of Valuations_in A
for S being Element of CQC-Sub-WFF holds
( not J,v . (Val_S (v,S)) |= S iff J,v . (Val_S (v,S)) |= Sub_not S )
let J be interpretation of A; :: thesis: for v being Element of Valuations_in A
for S being Element of CQC-Sub-WFF holds
( not J,v . (Val_S (v,S)) |= S iff J,v . (Val_S (v,S)) |= Sub_not S )
let v be Element of Valuations_in A; :: thesis: for S being Element of CQC-Sub-WFF holds
( not J,v . (Val_S (v,S)) |= S iff J,v . (Val_S (v,S)) |= Sub_not S )
let S be Element of CQC-Sub-WFF ; :: thesis: ( not J,v . (Val_S (v,S)) |= S iff J,v . (Val_S (v,S)) |= Sub_not S )
A1: ( not J,v . (Val_S (v,S)) |= S `1 iff J,v . (Val_S (v,S)) |= 'not' (S `1) ) by VALUAT_1:17;
( J,v . (Val_S (v,S)) |= 'not' (S `1) iff J,v . (Val_S (v,S)) |= (Sub_not S) `1 ) by Th17;
hence ( not J,v . (Val_S (v,S)) |= S iff J,v . (Val_S (v,S)) |= Sub_not S ) by A1, Def3; :: thesis: verum